Title A dynamic priority-based approach to concurrent toolpathplanning for multi-material layered manufacturing

Author(s) Choi SH Zhu WK

Citation Cad Computer Aided Design 2010 v 42 n 12 p 1095-1107

Issued Date 2010

URL httphdlhandlenet10722134406

Rights

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 40 International LicenseNOTICE this is the authorrsquos version of a work that was acceptedfor publication in Computer-Aided Design Changes resultingfrom the publishing process such as peer review editingcorrections structural formatting and other quality controlmechanisms may not be reflected in this document Changesmay have been made to this work since it was submitted forpublication A definitive version was subsequently published inComputer-Aided Design 2010 v 42 n 12 p 1095-1107 DOI101016jcad201007004

1

A Dynamic Priority-based Approach to Concurrent Toolpath

Planning for Multi-Material Layered Manufacturing

SH Choi and WK Zhu

Department of Industrial and Manufacturing Systems Engineering

The University of Hong Kong

Pokfulam Road Hong Kong

Abstract

This paper presents an approach to concurrent toolpath planning for multi-material

layered manufacturing (MMLM) to improve the fabrication efficiency of relatively

complex prototypes The approach is based on decoupled motion planning for multiple

moving objects in which the toolpaths of a set of tools are independently planned and

then coordinated to deposit materials concurrently Relative tool positions are

monitored and potential tool collisions detected at a predefined rate When a potential

collision between a pair of tools is detected a dynamic priority scheme is applied to

assign motion priorities of tools The traverse speeds of tools along the x-axis are

compared and a higher priority is assigned to the tool at a higher traverse speed A tool

with a higher priority continues to deposit material along its original path while the

one with a lower priority gives way by pausing at a suitable point until the potential

collision is eliminated Moreover the deposition speeds of tools can be adjusted to suit

different material properties and fabrication requirements The proposed approach has

been incorporated in a multi-material virtual prototyping (MMVP) system Digital

fabrication of prototypes shows that it can substantially shorten the fabrication time of

relatively complex multi-material objects The approach can be adapted for process

control of MMLM when appropriate hardware becomes available It is expected to

benefit various applications such as advanced product manufacturing and biomedical

fabrication

Key words

Layered manufacturing multi-materials toolpath planning multi-object motion

planning dynamic priority

2

1 Introduction

11 Layered Manufacturing

Layered manufacturing (LM) or rapid prototyping (RP) is an additive process that

fabricates a physical prototype from a CAD model layer by layer more rapidly than

conventional manufacturing processes [1] LM technology is now seen in a wide range

of applications such as product development biomedical engineering and architecture

etc It offers huge potential to reduce or eliminate some stages of the traditional supply

chain The global market for LM products and services grew to an estimated

USD1183 billion in 2008 and the LM industry is expected to more than double in size

by 2015 according to Wohlers Report 2009 [2]

LM processes can be roughly categorised as vector-based or raster-based While a

vector-based LM process drives a tool along a predefined path to deposit fabrication

material a raster-based process selectively generates specific contours out of an entire

layer of material Each of these LM processes offers distinctive traits for some specific

types of prototypes [3]

Although LM can shorten prototyping cycles the process is not as rapid as desired

Wohlers [2] pointed out that applications of LM are increasing yet current LM systems

are becoming unacceptably slow in respect of the increasing size and complexity of

prototypes being made Kochan [4] claimed that one of the main limitations of rapid

prototyping was the low speed at which a part was fabricated Bellini [5] presented

that Fused Deposition Modelling (FDM) was fast enough for small parts of a few cubic

inches or those of tall thin features but it could be very time-consuming for parts with

wide cross-sections Hauser et al [6] also pointed out that the methodology of LM

was essentially a start-stop process because each layer was processed and deposited

sequentially The breaks in the build cycles for example the positioning of hardware

often slowed down the build rate

Some efforts have been devoted to enhancing the fabrication efficiency of LM

Sintermask Technologies [7] developed a machine with a Selective Mask Sintering

(SMS) process capable of projecting infrared radiation through masks to sinter a whole

layer of polyamide powder in ten seconds Voxeljet [8] introduced a plastic powder

binding system capable of building 400 cubic inches per hour Hauser et al [6]

3

developed a software system to control a process called spiral growth manufacturing

(SGM) capable of building ten layers per minute Despite these developments most

commercial LM machines are still slow for relatively large and complex prototypes

12 Multi-Material Layered Manufacturing

Another major problem is that most LM machines to date can only fabricate

homogeneous prototypes of a single material However recent trends in various

industries particularly advanced product development [9] and biomedical engineering

[10] have warranted heterogeneous objects which offer superior properties

unparalleled by homogeneous ones [1] Heterogeneous objects may be classified into

two major types namely discrete multi-material (DMM) objects with a collection of

distinct materials divided by clear boundaries and functionally graded multi-material

(FGM) objects with materials that change gradually from one type to another [11]

There is indeed an imminent need to develop multi-material layered manufacturing

(MMLM) for fabrication of heterogeneous objects and some pioneering works have

been reported in recent years

Qiu et al [12] developed a virtual simulation system for fabrication of parts consisting

of discrete materials a toolpath planning method for two materials was reported to

reduce defects and voids of a virtual part Jepson [13] developed an experimental

MMLM machine which could blend two types of metallic powders to form a layer of

some material gradients and subsequently sinter it to build an FGM part Cho et al [14]

extended their patent ldquo3D printingrdquo to fabricate FGM parts two materials were

dispersed through their respective inkjet tools and printed into the powder bed Khalil

et al [10] developed a multi-nozzle biopolymer deposition system which was capable

of extruding biopolymer solutions and living cells for freeform construction of tissue

scaffolds Cesarano III [15] developed a so-called Robocasting technology which

was able to fabricate either single material or multi-material ceramic parts By turning

the blender on or off fabrication of graded alumina metal composites and discrete

placement of fugitive materials could be achieved Inamdar et al [16] developed a

multiple material stereolithography machine The mechanism consisted of three vats

each of which contained a specific material and a customised LabVIEW system was

used to control the rotating multiple vat system to fabricate a multi-material model

Wang and Shaw [17] introduced a method for fabricating functionally graded materials

4

via inkjet colour printing The print heads dispatched Al2O3 and ZrO2 aqueous

suspensions in different quantities to form a particular composition Malone et al [18]

developed the FabHome multi-material 3D printer for fabrication of

electro-mechanical systems Typical materials included polypropylene and ABS

thermoplastics and low melting-point metal alloys such as lead and tin A Zn-air cell

battery of about the size of a coin composed of five layers of different materials in a

plastic case was fabricated Objet Geometries Ltd [19] claimed that its Connex350

offered the ability to fabricate assemblies made of two types of photopolymer materials

with different mechanical properties The photopolymer materials were cured by

ultra-violet light immediately after jetting

These systems have made significant contributions to the development of MMLM

although they were mostly experimental and could only make simple prototypes of a

few types of materials However practical and viable MMLM systems for relatively

large complex objects have yet to be developed

It can be said that development of MMLM is mainly concerned with three major

research issues namely (1) fabrication materials (2) hardware mechanism for

deposition of materials and (3) computer software for planning the toolpaths and

subsequent process control of multiple tools for prototype fabrication These three

issues are generally studied by researchers of specialised expertise Nevertheless the

software issue of toolpath planning is particularly important as it has a significant

impact on the overall efficiency and quality of fabrication especially of large and

complex prototypes

13 Issues of Toolpath Planning

Toolpath planning for LM is mainly concerned with (i) contour filling strategy and (ii)

tool sequencing strategy [20] Contour filling strategy concerns mainly with how to

fill up the internal area of a contour This issue has been well-studied and standard

contour-filling patterns have been developed for LM [21] On the other hand tool

sequencing strategy is more about coordinating the motions of a set of tools each of

which deposits a material on specific contours to fabricate a multi-material prototype

safely and effectively Tool collisions and fabrication efficiency are main

considerations which may be exacerbated by the need to vary the tool deposition

5

speeds to suit different material properties and fabrication requirements [22] Tools

can be planned to deposit materials either sequentially to avoid collisions at the

expense of fabrication efficiency or concurrently to enhance fabrication efficiency

with risks of collisions This is a difficult problem of MMLM

Few research works on toolpath planning for MMLM have been reported Qiu et al

[12] developed a simulation system for toolpath analysis of MMLM In the system a

toolpath file per material was generated first and then integrated into one

multi-material toolpath file A toolpath planning method for two materials was reported

to reduce the defects and voids of a virtual part This method could process relatively

simple objects such as cylinder and cube Zhu and Yu [23] proposed a collision

detection and tool sequencing method for simple multi-material assemblies Zhou [24]

proposed a toolpath planning algorithm for fabrication of functionally graded

multi-material (FGM) objects First the gradual material distribution in each layer was

discretised into step-wise sub-regions in each of which the material could be assumed

homogeneous Then sequential toolpath for each sub-region was generated separately

The experimental MMLM systems described in the previous section also involved

some basic toolpath planning algorithms which were either sequential or could only

handle relatively simple prototypes Choi and Cheung [25] developed a multi-material

virtual prototyping system integrated with a topological hierarchy-based approach to

toolpath planning for MMLM This approach was later improved with an entire

envelope-based approach [20] and with a separate envelope-based approach [26]

These approaches were characterised by the construction of bounding envelopes

around slice contours by offsetting outward a distance of the tool radius Overlap test

was executed for these envelopes Tools in the non-overlapped envelopes could deposit

their specific materials concurrently without any collisions Nevertheless they did not

allow tools to move concurrently when the associated envelopes of the contours

overlapped incurring some idle time of tools

14 Research Objective

It can be concluded that toolpath planning for MMLM remains a vital but difficult

research issue which has yet to be fully tackled This paper therefore proposes a new

approach to concurrent toolpath planning for MMLM to further improve the

6

fabrication efficiency of relatively large complex prototypes This approach eradicates

the associated constraints of the previous approaches [20 25 26] to further improve

the fabrication efficiency It is characterised by construction of envelopes around

individual tools directly rather than around the slice contours of each layer Relative

tool positions are monitored to detect potential collisions at a predefined rate A

dynamic priority assignment scheme is applied to assign motion priorities of the tools

to avoid collisions and to coordinate the tool motions accordingly Deposition speeds

of tools can also be adjusted to suit different material properties and fabrication

requirements This concurrent toolpath planning approach can substantially shorten the

build-time of MMLM in comparison with the previous approaches

2 Related Works

21 Collision Detection

Tool collision is a major obstacle of multi-toolpath planning Collision detection also

known as interference detection or contact determination is an interdisciplinary issue

which is particularly important in motion planning robotics CADCAM etc [27]

Detection accuracy and computation cost are two inherently contradictory factors The

rate of collision detection is quite application-specific For instance haptic interfaces

require update rates of about one thousand hertz while about twenty to thirty updates

per second would be sufficient for real-time graphical applications [28] A number of

application-specific and practical collision detection algorithms have been proposed

and each of them has its own merits and deficiencies [29]

22 Multi-Object Motion Planning

In an MMLM process a number of tools deposit materials on specific contours to

fabricate a prototype preferably in concurrent motion to increase efficiency It can be

regarded as a more general control problem of multiple mobile objects sharing a

common workspace to complete their individual tasks without collision This problem

has received a great deal of attention in other applications such as mobile robots [30]

manipulation of robot arms [31] route planning for vehicles in a warehouse [32] etc

A variety of methods have been proposed to solve the multi-object motion planning

problem in which avoidance of collisions is paramount for safety and effectiveness In

7

general potential collisions are first detected and the object motions are subsequently

coordinated to avoid collisions and to improve optimality Optimisation objectives

include the minimisation of energy path length and motion time Indeed practicality

often demands a good balance between optimality (solution quality) and complexity

(computation cost) A broad review of multi-object motion planning can be found in

Lavalle‟s work [33] and this problem may be roughly categorised into coupled and

decoupled [34] as follows

221 Coupled Methods

A coupled method for multi-object motion planning combines the configuration spaces

of all the objects into a composite configuration space in which a feasible path is

searched for [32] In general it can achieve completeness and optimality However

the composite configuration space grows exponentially with the number of objects [35]

rendering the problem PSPACE-hard [36] Lavalle and Hutchinson [37] worked on

simultaneous optimisation of the motions of three robots from the start points to the

goals Li and Latombe [31] presented an approach to concurrent manipulation of two

robot arms to grab parts of various types on a conveyor and transfer them to their

respective goals while avoiding collisions with obstacles These works were among

early applications of coupled multi-object motion planning techniques on relatively

simple systems Indeed coupled methods are often used in systems with only a few

objects or for off-line applications

222 Decoupled Methods

In a decoupled method on the other hand the path of each object is separately

generated and subsequently coordinated to avoid collision [32] Different decoupled

methods have been applied to coordinate the motion of multiple objects including

adjustment of geometric paths modification of velocities and time delay [34] Wagner

et al [30] demonstrated an efficient approach to coordinating a group of cooperative

cleaner robots to clean a common dirty floor Lee and Kim [38] developed a

multi-robot printing system in which the host computer commanded a set of client

printer-robots to cooperatively draw a picture on a sheet of paper In the work of Peng

and Akella [39] the path of each robot was first generated irrespective of other robots

while the velocities were subsequently altered along their paths to avoid collision

Rekleitis et al [40] presented an algorithm to control a team of robots moving in

8

zigzags to complete the coverage of a 2D plane Lee et al [41] used potential

functions to guide objects to their destinations Chang et al [42] used a time delay

method to avoid collisions between two robot arms The minimum delay time needed

for collision avoidance was obtained by a collision map scheme

In essence decoupled methods involve assigning priorities to objects to determine the

order in which the paths are to be coordinated [43] Erdmann and Perez [44] assigned

static priority to each robot and sequentially computed paths in a time-varying

configuration space Ferrari et al [45] used a fixed priority scheme and chose random

detours for the robots with lower priorities These static priority schemes were suitable

for predefined applications On the other hand dynamic priority schemes are more

flexible to handle different situations Azarm and Schmidt [46] proposed an approach

that considered all possible priority assignments for up to three robots Clark et al [47]

presented a motion planning system that could construct collision-free paths for groups

of robots in dynamic environments They introduced a priority scheme that gave way

to the robot whose local workspace was most crowded Bennewitz et al [35] optimised

different possible priority schemes for teams of mobile robots Unfortunately

searching different sequences of priorities was computation-intensive and might fail to

find solutions to complex planning problems van den Berg and Overmars [43]

proposed a heuristic for assigning priorities to a team of robots in which a higher

priority was assigned to a robot with a longer moving distance Decoupled methods

often adopt priority-based approaches due to its prioritisation essence [35] They are

computationally simpler and can response faster in real-time applications in

comparison with coupled methods although they cannot guarantee optimal solutions

Moreover they are scalable for handling more mobile objects [32]

Based on the review above a dynamic priority-based decoupled method is proposed to

generate concurrent toolpaths for MMLM However MMLM has its distinct

characteristics with respect to multi-object motion planning First the tools do not have

self-control and sensing capabilities and they cannot communicate with each other

They are coordinated by a central controller Second the tools are normally

constrained to move along fixed paths of zigzags or spirals at constant deposition

speeds And third the toolpath planning approach for MMLM should take into account

the mechanical and thermal properties of the fabrication materials Hence the

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

1

A Dynamic Priority-based Approach to Concurrent Toolpath

Planning for Multi-Material Layered Manufacturing

SH Choi and WK Zhu

Department of Industrial and Manufacturing Systems Engineering

The University of Hong Kong

Pokfulam Road Hong Kong

Abstract

This paper presents an approach to concurrent toolpath planning for multi-material

layered manufacturing (MMLM) to improve the fabrication efficiency of relatively

complex prototypes The approach is based on decoupled motion planning for multiple

moving objects in which the toolpaths of a set of tools are independently planned and

then coordinated to deposit materials concurrently Relative tool positions are

monitored and potential tool collisions detected at a predefined rate When a potential

collision between a pair of tools is detected a dynamic priority scheme is applied to

assign motion priorities of tools The traverse speeds of tools along the x-axis are

compared and a higher priority is assigned to the tool at a higher traverse speed A tool

with a higher priority continues to deposit material along its original path while the

one with a lower priority gives way by pausing at a suitable point until the potential

collision is eliminated Moreover the deposition speeds of tools can be adjusted to suit

different material properties and fabrication requirements The proposed approach has

been incorporated in a multi-material virtual prototyping (MMVP) system Digital

fabrication of prototypes shows that it can substantially shorten the fabrication time of

relatively complex multi-material objects The approach can be adapted for process

control of MMLM when appropriate hardware becomes available It is expected to

benefit various applications such as advanced product manufacturing and biomedical

fabrication

Key words

Layered manufacturing multi-materials toolpath planning multi-object motion

planning dynamic priority

2

1 Introduction

11 Layered Manufacturing

Layered manufacturing (LM) or rapid prototyping (RP) is an additive process that

fabricates a physical prototype from a CAD model layer by layer more rapidly than

conventional manufacturing processes [1] LM technology is now seen in a wide range

of applications such as product development biomedical engineering and architecture

etc It offers huge potential to reduce or eliminate some stages of the traditional supply

chain The global market for LM products and services grew to an estimated

USD1183 billion in 2008 and the LM industry is expected to more than double in size

by 2015 according to Wohlers Report 2009 [2]

LM processes can be roughly categorised as vector-based or raster-based While a

vector-based LM process drives a tool along a predefined path to deposit fabrication

material a raster-based process selectively generates specific contours out of an entire

layer of material Each of these LM processes offers distinctive traits for some specific

types of prototypes [3]

Although LM can shorten prototyping cycles the process is not as rapid as desired

Wohlers [2] pointed out that applications of LM are increasing yet current LM systems

are becoming unacceptably slow in respect of the increasing size and complexity of

prototypes being made Kochan [4] claimed that one of the main limitations of rapid

prototyping was the low speed at which a part was fabricated Bellini [5] presented

that Fused Deposition Modelling (FDM) was fast enough for small parts of a few cubic

inches or those of tall thin features but it could be very time-consuming for parts with

wide cross-sections Hauser et al [6] also pointed out that the methodology of LM

was essentially a start-stop process because each layer was processed and deposited

sequentially The breaks in the build cycles for example the positioning of hardware

often slowed down the build rate

Some efforts have been devoted to enhancing the fabrication efficiency of LM

Sintermask Technologies [7] developed a machine with a Selective Mask Sintering

(SMS) process capable of projecting infrared radiation through masks to sinter a whole

layer of polyamide powder in ten seconds Voxeljet [8] introduced a plastic powder

binding system capable of building 400 cubic inches per hour Hauser et al [6]

3

developed a software system to control a process called spiral growth manufacturing

(SGM) capable of building ten layers per minute Despite these developments most

commercial LM machines are still slow for relatively large and complex prototypes

12 Multi-Material Layered Manufacturing

Another major problem is that most LM machines to date can only fabricate

homogeneous prototypes of a single material However recent trends in various

industries particularly advanced product development [9] and biomedical engineering

[10] have warranted heterogeneous objects which offer superior properties

unparalleled by homogeneous ones [1] Heterogeneous objects may be classified into

two major types namely discrete multi-material (DMM) objects with a collection of

distinct materials divided by clear boundaries and functionally graded multi-material

(FGM) objects with materials that change gradually from one type to another [11]

There is indeed an imminent need to develop multi-material layered manufacturing

(MMLM) for fabrication of heterogeneous objects and some pioneering works have

been reported in recent years

Qiu et al [12] developed a virtual simulation system for fabrication of parts consisting

of discrete materials a toolpath planning method for two materials was reported to

reduce defects and voids of a virtual part Jepson [13] developed an experimental

MMLM machine which could blend two types of metallic powders to form a layer of

some material gradients and subsequently sinter it to build an FGM part Cho et al [14]

extended their patent ldquo3D printingrdquo to fabricate FGM parts two materials were

dispersed through their respective inkjet tools and printed into the powder bed Khalil

et al [10] developed a multi-nozzle biopolymer deposition system which was capable

of extruding biopolymer solutions and living cells for freeform construction of tissue

scaffolds Cesarano III [15] developed a so-called Robocasting technology which

was able to fabricate either single material or multi-material ceramic parts By turning

the blender on or off fabrication of graded alumina metal composites and discrete

placement of fugitive materials could be achieved Inamdar et al [16] developed a

multiple material stereolithography machine The mechanism consisted of three vats

each of which contained a specific material and a customised LabVIEW system was

used to control the rotating multiple vat system to fabricate a multi-material model

Wang and Shaw [17] introduced a method for fabricating functionally graded materials

4

via inkjet colour printing The print heads dispatched Al2O3 and ZrO2 aqueous

suspensions in different quantities to form a particular composition Malone et al [18]

developed the FabHome multi-material 3D printer for fabrication of

electro-mechanical systems Typical materials included polypropylene and ABS

thermoplastics and low melting-point metal alloys such as lead and tin A Zn-air cell

battery of about the size of a coin composed of five layers of different materials in a

plastic case was fabricated Objet Geometries Ltd [19] claimed that its Connex350

offered the ability to fabricate assemblies made of two types of photopolymer materials

with different mechanical properties The photopolymer materials were cured by

ultra-violet light immediately after jetting

These systems have made significant contributions to the development of MMLM

although they were mostly experimental and could only make simple prototypes of a

few types of materials However practical and viable MMLM systems for relatively

large complex objects have yet to be developed

It can be said that development of MMLM is mainly concerned with three major

research issues namely (1) fabrication materials (2) hardware mechanism for

deposition of materials and (3) computer software for planning the toolpaths and

subsequent process control of multiple tools for prototype fabrication These three

issues are generally studied by researchers of specialised expertise Nevertheless the

software issue of toolpath planning is particularly important as it has a significant

impact on the overall efficiency and quality of fabrication especially of large and

complex prototypes

13 Issues of Toolpath Planning

Toolpath planning for LM is mainly concerned with (i) contour filling strategy and (ii)

tool sequencing strategy [20] Contour filling strategy concerns mainly with how to

fill up the internal area of a contour This issue has been well-studied and standard

contour-filling patterns have been developed for LM [21] On the other hand tool

sequencing strategy is more about coordinating the motions of a set of tools each of

which deposits a material on specific contours to fabricate a multi-material prototype

safely and effectively Tool collisions and fabrication efficiency are main

considerations which may be exacerbated by the need to vary the tool deposition

5

speeds to suit different material properties and fabrication requirements [22] Tools

can be planned to deposit materials either sequentially to avoid collisions at the

expense of fabrication efficiency or concurrently to enhance fabrication efficiency

with risks of collisions This is a difficult problem of MMLM

Few research works on toolpath planning for MMLM have been reported Qiu et al

[12] developed a simulation system for toolpath analysis of MMLM In the system a

toolpath file per material was generated first and then integrated into one

multi-material toolpath file A toolpath planning method for two materials was reported

to reduce the defects and voids of a virtual part This method could process relatively

simple objects such as cylinder and cube Zhu and Yu [23] proposed a collision

detection and tool sequencing method for simple multi-material assemblies Zhou [24]

proposed a toolpath planning algorithm for fabrication of functionally graded

multi-material (FGM) objects First the gradual material distribution in each layer was

discretised into step-wise sub-regions in each of which the material could be assumed

homogeneous Then sequential toolpath for each sub-region was generated separately

The experimental MMLM systems described in the previous section also involved

some basic toolpath planning algorithms which were either sequential or could only

handle relatively simple prototypes Choi and Cheung [25] developed a multi-material

virtual prototyping system integrated with a topological hierarchy-based approach to

toolpath planning for MMLM This approach was later improved with an entire

envelope-based approach [20] and with a separate envelope-based approach [26]

These approaches were characterised by the construction of bounding envelopes

around slice contours by offsetting outward a distance of the tool radius Overlap test

was executed for these envelopes Tools in the non-overlapped envelopes could deposit

their specific materials concurrently without any collisions Nevertheless they did not

allow tools to move concurrently when the associated envelopes of the contours

overlapped incurring some idle time of tools

14 Research Objective

It can be concluded that toolpath planning for MMLM remains a vital but difficult

research issue which has yet to be fully tackled This paper therefore proposes a new

approach to concurrent toolpath planning for MMLM to further improve the

6

fabrication efficiency of relatively large complex prototypes This approach eradicates

the associated constraints of the previous approaches [20 25 26] to further improve

the fabrication efficiency It is characterised by construction of envelopes around

individual tools directly rather than around the slice contours of each layer Relative

tool positions are monitored to detect potential collisions at a predefined rate A

dynamic priority assignment scheme is applied to assign motion priorities of the tools

to avoid collisions and to coordinate the tool motions accordingly Deposition speeds

of tools can also be adjusted to suit different material properties and fabrication

requirements This concurrent toolpath planning approach can substantially shorten the

build-time of MMLM in comparison with the previous approaches

2 Related Works

21 Collision Detection

Tool collision is a major obstacle of multi-toolpath planning Collision detection also

known as interference detection or contact determination is an interdisciplinary issue

which is particularly important in motion planning robotics CADCAM etc [27]

Detection accuracy and computation cost are two inherently contradictory factors The

rate of collision detection is quite application-specific For instance haptic interfaces

require update rates of about one thousand hertz while about twenty to thirty updates

per second would be sufficient for real-time graphical applications [28] A number of

application-specific and practical collision detection algorithms have been proposed

and each of them has its own merits and deficiencies [29]

22 Multi-Object Motion Planning

In an MMLM process a number of tools deposit materials on specific contours to

fabricate a prototype preferably in concurrent motion to increase efficiency It can be

regarded as a more general control problem of multiple mobile objects sharing a

common workspace to complete their individual tasks without collision This problem

has received a great deal of attention in other applications such as mobile robots [30]

manipulation of robot arms [31] route planning for vehicles in a warehouse [32] etc

A variety of methods have been proposed to solve the multi-object motion planning

problem in which avoidance of collisions is paramount for safety and effectiveness In

7

general potential collisions are first detected and the object motions are subsequently

coordinated to avoid collisions and to improve optimality Optimisation objectives

include the minimisation of energy path length and motion time Indeed practicality

often demands a good balance between optimality (solution quality) and complexity

(computation cost) A broad review of multi-object motion planning can be found in

Lavalle‟s work [33] and this problem may be roughly categorised into coupled and

decoupled [34] as follows

221 Coupled Methods

A coupled method for multi-object motion planning combines the configuration spaces

of all the objects into a composite configuration space in which a feasible path is

searched for [32] In general it can achieve completeness and optimality However

the composite configuration space grows exponentially with the number of objects [35]

rendering the problem PSPACE-hard [36] Lavalle and Hutchinson [37] worked on

simultaneous optimisation of the motions of three robots from the start points to the

goals Li and Latombe [31] presented an approach to concurrent manipulation of two

robot arms to grab parts of various types on a conveyor and transfer them to their

respective goals while avoiding collisions with obstacles These works were among

early applications of coupled multi-object motion planning techniques on relatively

simple systems Indeed coupled methods are often used in systems with only a few

objects or for off-line applications

222 Decoupled Methods

In a decoupled method on the other hand the path of each object is separately

generated and subsequently coordinated to avoid collision [32] Different decoupled

methods have been applied to coordinate the motion of multiple objects including

adjustment of geometric paths modification of velocities and time delay [34] Wagner

et al [30] demonstrated an efficient approach to coordinating a group of cooperative

cleaner robots to clean a common dirty floor Lee and Kim [38] developed a

multi-robot printing system in which the host computer commanded a set of client

printer-robots to cooperatively draw a picture on a sheet of paper In the work of Peng

and Akella [39] the path of each robot was first generated irrespective of other robots

while the velocities were subsequently altered along their paths to avoid collision

Rekleitis et al [40] presented an algorithm to control a team of robots moving in

8

zigzags to complete the coverage of a 2D plane Lee et al [41] used potential

functions to guide objects to their destinations Chang et al [42] used a time delay

method to avoid collisions between two robot arms The minimum delay time needed

for collision avoidance was obtained by a collision map scheme

In essence decoupled methods involve assigning priorities to objects to determine the

order in which the paths are to be coordinated [43] Erdmann and Perez [44] assigned

static priority to each robot and sequentially computed paths in a time-varying

configuration space Ferrari et al [45] used a fixed priority scheme and chose random

detours for the robots with lower priorities These static priority schemes were suitable

for predefined applications On the other hand dynamic priority schemes are more

flexible to handle different situations Azarm and Schmidt [46] proposed an approach

that considered all possible priority assignments for up to three robots Clark et al [47]

presented a motion planning system that could construct collision-free paths for groups

of robots in dynamic environments They introduced a priority scheme that gave way

to the robot whose local workspace was most crowded Bennewitz et al [35] optimised

different possible priority schemes for teams of mobile robots Unfortunately

searching different sequences of priorities was computation-intensive and might fail to

find solutions to complex planning problems van den Berg and Overmars [43]

proposed a heuristic for assigning priorities to a team of robots in which a higher

priority was assigned to a robot with a longer moving distance Decoupled methods

often adopt priority-based approaches due to its prioritisation essence [35] They are

computationally simpler and can response faster in real-time applications in

comparison with coupled methods although they cannot guarantee optimal solutions

Moreover they are scalable for handling more mobile objects [32]

Based on the review above a dynamic priority-based decoupled method is proposed to

generate concurrent toolpaths for MMLM However MMLM has its distinct

characteristics with respect to multi-object motion planning First the tools do not have

self-control and sensing capabilities and they cannot communicate with each other

They are coordinated by a central controller Second the tools are normally

constrained to move along fixed paths of zigzags or spirals at constant deposition

speeds And third the toolpath planning approach for MMLM should take into account

the mechanical and thermal properties of the fabrication materials Hence the

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

2

1 Introduction

11 Layered Manufacturing

Layered manufacturing (LM) or rapid prototyping (RP) is an additive process that

fabricates a physical prototype from a CAD model layer by layer more rapidly than

conventional manufacturing processes [1] LM technology is now seen in a wide range

of applications such as product development biomedical engineering and architecture

etc It offers huge potential to reduce or eliminate some stages of the traditional supply

chain The global market for LM products and services grew to an estimated

USD1183 billion in 2008 and the LM industry is expected to more than double in size

by 2015 according to Wohlers Report 2009 [2]

LM processes can be roughly categorised as vector-based or raster-based While a

vector-based LM process drives a tool along a predefined path to deposit fabrication

material a raster-based process selectively generates specific contours out of an entire

layer of material Each of these LM processes offers distinctive traits for some specific

types of prototypes [3]

Although LM can shorten prototyping cycles the process is not as rapid as desired

Wohlers [2] pointed out that applications of LM are increasing yet current LM systems

are becoming unacceptably slow in respect of the increasing size and complexity of

prototypes being made Kochan [4] claimed that one of the main limitations of rapid

prototyping was the low speed at which a part was fabricated Bellini [5] presented

that Fused Deposition Modelling (FDM) was fast enough for small parts of a few cubic

inches or those of tall thin features but it could be very time-consuming for parts with

wide cross-sections Hauser et al [6] also pointed out that the methodology of LM

was essentially a start-stop process because each layer was processed and deposited

sequentially The breaks in the build cycles for example the positioning of hardware

often slowed down the build rate

Some efforts have been devoted to enhancing the fabrication efficiency of LM

Sintermask Technologies [7] developed a machine with a Selective Mask Sintering

(SMS) process capable of projecting infrared radiation through masks to sinter a whole

layer of polyamide powder in ten seconds Voxeljet [8] introduced a plastic powder

binding system capable of building 400 cubic inches per hour Hauser et al [6]

3

developed a software system to control a process called spiral growth manufacturing

(SGM) capable of building ten layers per minute Despite these developments most

commercial LM machines are still slow for relatively large and complex prototypes

12 Multi-Material Layered Manufacturing

Another major problem is that most LM machines to date can only fabricate

homogeneous prototypes of a single material However recent trends in various

industries particularly advanced product development [9] and biomedical engineering

[10] have warranted heterogeneous objects which offer superior properties

unparalleled by homogeneous ones [1] Heterogeneous objects may be classified into

two major types namely discrete multi-material (DMM) objects with a collection of

distinct materials divided by clear boundaries and functionally graded multi-material

(FGM) objects with materials that change gradually from one type to another [11]

There is indeed an imminent need to develop multi-material layered manufacturing

(MMLM) for fabrication of heterogeneous objects and some pioneering works have

been reported in recent years

Qiu et al [12] developed a virtual simulation system for fabrication of parts consisting

of discrete materials a toolpath planning method for two materials was reported to

reduce defects and voids of a virtual part Jepson [13] developed an experimental

MMLM machine which could blend two types of metallic powders to form a layer of

some material gradients and subsequently sinter it to build an FGM part Cho et al [14]

extended their patent ldquo3D printingrdquo to fabricate FGM parts two materials were

dispersed through their respective inkjet tools and printed into the powder bed Khalil

et al [10] developed a multi-nozzle biopolymer deposition system which was capable

of extruding biopolymer solutions and living cells for freeform construction of tissue

scaffolds Cesarano III [15] developed a so-called Robocasting technology which

was able to fabricate either single material or multi-material ceramic parts By turning

the blender on or off fabrication of graded alumina metal composites and discrete

placement of fugitive materials could be achieved Inamdar et al [16] developed a

multiple material stereolithography machine The mechanism consisted of three vats

each of which contained a specific material and a customised LabVIEW system was

used to control the rotating multiple vat system to fabricate a multi-material model

Wang and Shaw [17] introduced a method for fabricating functionally graded materials

4

via inkjet colour printing The print heads dispatched Al2O3 and ZrO2 aqueous

suspensions in different quantities to form a particular composition Malone et al [18]

developed the FabHome multi-material 3D printer for fabrication of

electro-mechanical systems Typical materials included polypropylene and ABS

thermoplastics and low melting-point metal alloys such as lead and tin A Zn-air cell

battery of about the size of a coin composed of five layers of different materials in a

plastic case was fabricated Objet Geometries Ltd [19] claimed that its Connex350

offered the ability to fabricate assemblies made of two types of photopolymer materials

with different mechanical properties The photopolymer materials were cured by

ultra-violet light immediately after jetting

These systems have made significant contributions to the development of MMLM

although they were mostly experimental and could only make simple prototypes of a

few types of materials However practical and viable MMLM systems for relatively

large complex objects have yet to be developed

It can be said that development of MMLM is mainly concerned with three major

research issues namely (1) fabrication materials (2) hardware mechanism for

deposition of materials and (3) computer software for planning the toolpaths and

subsequent process control of multiple tools for prototype fabrication These three

issues are generally studied by researchers of specialised expertise Nevertheless the

software issue of toolpath planning is particularly important as it has a significant

impact on the overall efficiency and quality of fabrication especially of large and

complex prototypes

13 Issues of Toolpath Planning

Toolpath planning for LM is mainly concerned with (i) contour filling strategy and (ii)

tool sequencing strategy [20] Contour filling strategy concerns mainly with how to

fill up the internal area of a contour This issue has been well-studied and standard

contour-filling patterns have been developed for LM [21] On the other hand tool

sequencing strategy is more about coordinating the motions of a set of tools each of

which deposits a material on specific contours to fabricate a multi-material prototype

safely and effectively Tool collisions and fabrication efficiency are main

considerations which may be exacerbated by the need to vary the tool deposition

5

speeds to suit different material properties and fabrication requirements [22] Tools

can be planned to deposit materials either sequentially to avoid collisions at the

expense of fabrication efficiency or concurrently to enhance fabrication efficiency

with risks of collisions This is a difficult problem of MMLM

Few research works on toolpath planning for MMLM have been reported Qiu et al

[12] developed a simulation system for toolpath analysis of MMLM In the system a

toolpath file per material was generated first and then integrated into one

multi-material toolpath file A toolpath planning method for two materials was reported

to reduce the defects and voids of a virtual part This method could process relatively

simple objects such as cylinder and cube Zhu and Yu [23] proposed a collision

detection and tool sequencing method for simple multi-material assemblies Zhou [24]

proposed a toolpath planning algorithm for fabrication of functionally graded

multi-material (FGM) objects First the gradual material distribution in each layer was

discretised into step-wise sub-regions in each of which the material could be assumed

homogeneous Then sequential toolpath for each sub-region was generated separately

The experimental MMLM systems described in the previous section also involved

some basic toolpath planning algorithms which were either sequential or could only

handle relatively simple prototypes Choi and Cheung [25] developed a multi-material

virtual prototyping system integrated with a topological hierarchy-based approach to

toolpath planning for MMLM This approach was later improved with an entire

envelope-based approach [20] and with a separate envelope-based approach [26]

These approaches were characterised by the construction of bounding envelopes

around slice contours by offsetting outward a distance of the tool radius Overlap test

was executed for these envelopes Tools in the non-overlapped envelopes could deposit

their specific materials concurrently without any collisions Nevertheless they did not

allow tools to move concurrently when the associated envelopes of the contours

overlapped incurring some idle time of tools

14 Research Objective

It can be concluded that toolpath planning for MMLM remains a vital but difficult

research issue which has yet to be fully tackled This paper therefore proposes a new

approach to concurrent toolpath planning for MMLM to further improve the

6

fabrication efficiency of relatively large complex prototypes This approach eradicates

the associated constraints of the previous approaches [20 25 26] to further improve

the fabrication efficiency It is characterised by construction of envelopes around

individual tools directly rather than around the slice contours of each layer Relative

tool positions are monitored to detect potential collisions at a predefined rate A

dynamic priority assignment scheme is applied to assign motion priorities of the tools

to avoid collisions and to coordinate the tool motions accordingly Deposition speeds

of tools can also be adjusted to suit different material properties and fabrication

requirements This concurrent toolpath planning approach can substantially shorten the

build-time of MMLM in comparison with the previous approaches

2 Related Works

21 Collision Detection

Tool collision is a major obstacle of multi-toolpath planning Collision detection also

known as interference detection or contact determination is an interdisciplinary issue

which is particularly important in motion planning robotics CADCAM etc [27]

Detection accuracy and computation cost are two inherently contradictory factors The

rate of collision detection is quite application-specific For instance haptic interfaces

require update rates of about one thousand hertz while about twenty to thirty updates

per second would be sufficient for real-time graphical applications [28] A number of

application-specific and practical collision detection algorithms have been proposed

and each of them has its own merits and deficiencies [29]

22 Multi-Object Motion Planning

In an MMLM process a number of tools deposit materials on specific contours to

fabricate a prototype preferably in concurrent motion to increase efficiency It can be

regarded as a more general control problem of multiple mobile objects sharing a

common workspace to complete their individual tasks without collision This problem

has received a great deal of attention in other applications such as mobile robots [30]

manipulation of robot arms [31] route planning for vehicles in a warehouse [32] etc

A variety of methods have been proposed to solve the multi-object motion planning

problem in which avoidance of collisions is paramount for safety and effectiveness In

7

general potential collisions are first detected and the object motions are subsequently

coordinated to avoid collisions and to improve optimality Optimisation objectives

include the minimisation of energy path length and motion time Indeed practicality

often demands a good balance between optimality (solution quality) and complexity

(computation cost) A broad review of multi-object motion planning can be found in

Lavalle‟s work [33] and this problem may be roughly categorised into coupled and

decoupled [34] as follows

221 Coupled Methods

A coupled method for multi-object motion planning combines the configuration spaces

of all the objects into a composite configuration space in which a feasible path is

searched for [32] In general it can achieve completeness and optimality However

the composite configuration space grows exponentially with the number of objects [35]

rendering the problem PSPACE-hard [36] Lavalle and Hutchinson [37] worked on

simultaneous optimisation of the motions of three robots from the start points to the

goals Li and Latombe [31] presented an approach to concurrent manipulation of two

robot arms to grab parts of various types on a conveyor and transfer them to their

respective goals while avoiding collisions with obstacles These works were among

early applications of coupled multi-object motion planning techniques on relatively

simple systems Indeed coupled methods are often used in systems with only a few

objects or for off-line applications

222 Decoupled Methods

In a decoupled method on the other hand the path of each object is separately

generated and subsequently coordinated to avoid collision [32] Different decoupled

methods have been applied to coordinate the motion of multiple objects including

adjustment of geometric paths modification of velocities and time delay [34] Wagner

et al [30] demonstrated an efficient approach to coordinating a group of cooperative

cleaner robots to clean a common dirty floor Lee and Kim [38] developed a

multi-robot printing system in which the host computer commanded a set of client

printer-robots to cooperatively draw a picture on a sheet of paper In the work of Peng

and Akella [39] the path of each robot was first generated irrespective of other robots

while the velocities were subsequently altered along their paths to avoid collision

Rekleitis et al [40] presented an algorithm to control a team of robots moving in

8

zigzags to complete the coverage of a 2D plane Lee et al [41] used potential

functions to guide objects to their destinations Chang et al [42] used a time delay

method to avoid collisions between two robot arms The minimum delay time needed

for collision avoidance was obtained by a collision map scheme

In essence decoupled methods involve assigning priorities to objects to determine the

order in which the paths are to be coordinated [43] Erdmann and Perez [44] assigned

static priority to each robot and sequentially computed paths in a time-varying

configuration space Ferrari et al [45] used a fixed priority scheme and chose random

detours for the robots with lower priorities These static priority schemes were suitable

for predefined applications On the other hand dynamic priority schemes are more

flexible to handle different situations Azarm and Schmidt [46] proposed an approach

that considered all possible priority assignments for up to three robots Clark et al [47]

presented a motion planning system that could construct collision-free paths for groups

of robots in dynamic environments They introduced a priority scheme that gave way

to the robot whose local workspace was most crowded Bennewitz et al [35] optimised

different possible priority schemes for teams of mobile robots Unfortunately

searching different sequences of priorities was computation-intensive and might fail to

find solutions to complex planning problems van den Berg and Overmars [43]

proposed a heuristic for assigning priorities to a team of robots in which a higher

priority was assigned to a robot with a longer moving distance Decoupled methods

often adopt priority-based approaches due to its prioritisation essence [35] They are

computationally simpler and can response faster in real-time applications in

comparison with coupled methods although they cannot guarantee optimal solutions

Moreover they are scalable for handling more mobile objects [32]

Based on the review above a dynamic priority-based decoupled method is proposed to

generate concurrent toolpaths for MMLM However MMLM has its distinct

characteristics with respect to multi-object motion planning First the tools do not have

self-control and sensing capabilities and they cannot communicate with each other

They are coordinated by a central controller Second the tools are normally

constrained to move along fixed paths of zigzags or spirals at constant deposition

speeds And third the toolpath planning approach for MMLM should take into account

the mechanical and thermal properties of the fabrication materials Hence the

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

3

developed a software system to control a process called spiral growth manufacturing

(SGM) capable of building ten layers per minute Despite these developments most

commercial LM machines are still slow for relatively large and complex prototypes

12 Multi-Material Layered Manufacturing

Another major problem is that most LM machines to date can only fabricate

homogeneous prototypes of a single material However recent trends in various

industries particularly advanced product development [9] and biomedical engineering

[10] have warranted heterogeneous objects which offer superior properties

unparalleled by homogeneous ones [1] Heterogeneous objects may be classified into

two major types namely discrete multi-material (DMM) objects with a collection of

distinct materials divided by clear boundaries and functionally graded multi-material

(FGM) objects with materials that change gradually from one type to another [11]

There is indeed an imminent need to develop multi-material layered manufacturing

(MMLM) for fabrication of heterogeneous objects and some pioneering works have

been reported in recent years

Qiu et al [12] developed a virtual simulation system for fabrication of parts consisting

of discrete materials a toolpath planning method for two materials was reported to

reduce defects and voids of a virtual part Jepson [13] developed an experimental

MMLM machine which could blend two types of metallic powders to form a layer of

some material gradients and subsequently sinter it to build an FGM part Cho et al [14]

extended their patent ldquo3D printingrdquo to fabricate FGM parts two materials were

dispersed through their respective inkjet tools and printed into the powder bed Khalil

et al [10] developed a multi-nozzle biopolymer deposition system which was capable

of extruding biopolymer solutions and living cells for freeform construction of tissue

scaffolds Cesarano III [15] developed a so-called Robocasting technology which

was able to fabricate either single material or multi-material ceramic parts By turning

the blender on or off fabrication of graded alumina metal composites and discrete

placement of fugitive materials could be achieved Inamdar et al [16] developed a

multiple material stereolithography machine The mechanism consisted of three vats

each of which contained a specific material and a customised LabVIEW system was

used to control the rotating multiple vat system to fabricate a multi-material model

Wang and Shaw [17] introduced a method for fabricating functionally graded materials

4

via inkjet colour printing The print heads dispatched Al2O3 and ZrO2 aqueous

suspensions in different quantities to form a particular composition Malone et al [18]

developed the FabHome multi-material 3D printer for fabrication of

electro-mechanical systems Typical materials included polypropylene and ABS

thermoplastics and low melting-point metal alloys such as lead and tin A Zn-air cell

battery of about the size of a coin composed of five layers of different materials in a

plastic case was fabricated Objet Geometries Ltd [19] claimed that its Connex350

offered the ability to fabricate assemblies made of two types of photopolymer materials

with different mechanical properties The photopolymer materials were cured by

ultra-violet light immediately after jetting

These systems have made significant contributions to the development of MMLM

although they were mostly experimental and could only make simple prototypes of a

few types of materials However practical and viable MMLM systems for relatively

large complex objects have yet to be developed

It can be said that development of MMLM is mainly concerned with three major

research issues namely (1) fabrication materials (2) hardware mechanism for

deposition of materials and (3) computer software for planning the toolpaths and

subsequent process control of multiple tools for prototype fabrication These three

issues are generally studied by researchers of specialised expertise Nevertheless the

software issue of toolpath planning is particularly important as it has a significant

impact on the overall efficiency and quality of fabrication especially of large and

complex prototypes

13 Issues of Toolpath Planning

Toolpath planning for LM is mainly concerned with (i) contour filling strategy and (ii)

tool sequencing strategy [20] Contour filling strategy concerns mainly with how to

fill up the internal area of a contour This issue has been well-studied and standard

contour-filling patterns have been developed for LM [21] On the other hand tool

sequencing strategy is more about coordinating the motions of a set of tools each of

which deposits a material on specific contours to fabricate a multi-material prototype

safely and effectively Tool collisions and fabrication efficiency are main

considerations which may be exacerbated by the need to vary the tool deposition

5

speeds to suit different material properties and fabrication requirements [22] Tools

can be planned to deposit materials either sequentially to avoid collisions at the

expense of fabrication efficiency or concurrently to enhance fabrication efficiency

with risks of collisions This is a difficult problem of MMLM

Few research works on toolpath planning for MMLM have been reported Qiu et al

[12] developed a simulation system for toolpath analysis of MMLM In the system a

toolpath file per material was generated first and then integrated into one

multi-material toolpath file A toolpath planning method for two materials was reported

to reduce the defects and voids of a virtual part This method could process relatively

simple objects such as cylinder and cube Zhu and Yu [23] proposed a collision

detection and tool sequencing method for simple multi-material assemblies Zhou [24]

proposed a toolpath planning algorithm for fabrication of functionally graded

multi-material (FGM) objects First the gradual material distribution in each layer was

discretised into step-wise sub-regions in each of which the material could be assumed

homogeneous Then sequential toolpath for each sub-region was generated separately

The experimental MMLM systems described in the previous section also involved

some basic toolpath planning algorithms which were either sequential or could only

handle relatively simple prototypes Choi and Cheung [25] developed a multi-material

virtual prototyping system integrated with a topological hierarchy-based approach to

toolpath planning for MMLM This approach was later improved with an entire

envelope-based approach [20] and with a separate envelope-based approach [26]

These approaches were characterised by the construction of bounding envelopes

around slice contours by offsetting outward a distance of the tool radius Overlap test

was executed for these envelopes Tools in the non-overlapped envelopes could deposit

their specific materials concurrently without any collisions Nevertheless they did not

allow tools to move concurrently when the associated envelopes of the contours

overlapped incurring some idle time of tools

14 Research Objective

It can be concluded that toolpath planning for MMLM remains a vital but difficult

research issue which has yet to be fully tackled This paper therefore proposes a new

approach to concurrent toolpath planning for MMLM to further improve the

6

fabrication efficiency of relatively large complex prototypes This approach eradicates

the associated constraints of the previous approaches [20 25 26] to further improve

the fabrication efficiency It is characterised by construction of envelopes around

individual tools directly rather than around the slice contours of each layer Relative

tool positions are monitored to detect potential collisions at a predefined rate A

dynamic priority assignment scheme is applied to assign motion priorities of the tools

to avoid collisions and to coordinate the tool motions accordingly Deposition speeds

of tools can also be adjusted to suit different material properties and fabrication

requirements This concurrent toolpath planning approach can substantially shorten the

build-time of MMLM in comparison with the previous approaches

2 Related Works

21 Collision Detection

Tool collision is a major obstacle of multi-toolpath planning Collision detection also

known as interference detection or contact determination is an interdisciplinary issue

which is particularly important in motion planning robotics CADCAM etc [27]

Detection accuracy and computation cost are two inherently contradictory factors The

rate of collision detection is quite application-specific For instance haptic interfaces

require update rates of about one thousand hertz while about twenty to thirty updates

per second would be sufficient for real-time graphical applications [28] A number of

application-specific and practical collision detection algorithms have been proposed

and each of them has its own merits and deficiencies [29]

22 Multi-Object Motion Planning

In an MMLM process a number of tools deposit materials on specific contours to

fabricate a prototype preferably in concurrent motion to increase efficiency It can be

regarded as a more general control problem of multiple mobile objects sharing a

common workspace to complete their individual tasks without collision This problem

has received a great deal of attention in other applications such as mobile robots [30]

manipulation of robot arms [31] route planning for vehicles in a warehouse [32] etc

A variety of methods have been proposed to solve the multi-object motion planning

problem in which avoidance of collisions is paramount for safety and effectiveness In

7

general potential collisions are first detected and the object motions are subsequently

coordinated to avoid collisions and to improve optimality Optimisation objectives

include the minimisation of energy path length and motion time Indeed practicality

often demands a good balance between optimality (solution quality) and complexity

(computation cost) A broad review of multi-object motion planning can be found in

Lavalle‟s work [33] and this problem may be roughly categorised into coupled and

decoupled [34] as follows

221 Coupled Methods

A coupled method for multi-object motion planning combines the configuration spaces

of all the objects into a composite configuration space in which a feasible path is

searched for [32] In general it can achieve completeness and optimality However

the composite configuration space grows exponentially with the number of objects [35]

rendering the problem PSPACE-hard [36] Lavalle and Hutchinson [37] worked on

simultaneous optimisation of the motions of three robots from the start points to the

goals Li and Latombe [31] presented an approach to concurrent manipulation of two

robot arms to grab parts of various types on a conveyor and transfer them to their

respective goals while avoiding collisions with obstacles These works were among

early applications of coupled multi-object motion planning techniques on relatively

simple systems Indeed coupled methods are often used in systems with only a few

objects or for off-line applications

222 Decoupled Methods

In a decoupled method on the other hand the path of each object is separately

generated and subsequently coordinated to avoid collision [32] Different decoupled

methods have been applied to coordinate the motion of multiple objects including

adjustment of geometric paths modification of velocities and time delay [34] Wagner

et al [30] demonstrated an efficient approach to coordinating a group of cooperative

cleaner robots to clean a common dirty floor Lee and Kim [38] developed a

multi-robot printing system in which the host computer commanded a set of client

printer-robots to cooperatively draw a picture on a sheet of paper In the work of Peng

and Akella [39] the path of each robot was first generated irrespective of other robots

while the velocities were subsequently altered along their paths to avoid collision

Rekleitis et al [40] presented an algorithm to control a team of robots moving in

8

zigzags to complete the coverage of a 2D plane Lee et al [41] used potential

functions to guide objects to their destinations Chang et al [42] used a time delay

method to avoid collisions between two robot arms The minimum delay time needed

for collision avoidance was obtained by a collision map scheme

In essence decoupled methods involve assigning priorities to objects to determine the

order in which the paths are to be coordinated [43] Erdmann and Perez [44] assigned

static priority to each robot and sequentially computed paths in a time-varying

configuration space Ferrari et al [45] used a fixed priority scheme and chose random

detours for the robots with lower priorities These static priority schemes were suitable

for predefined applications On the other hand dynamic priority schemes are more

flexible to handle different situations Azarm and Schmidt [46] proposed an approach

that considered all possible priority assignments for up to three robots Clark et al [47]

presented a motion planning system that could construct collision-free paths for groups

of robots in dynamic environments They introduced a priority scheme that gave way

to the robot whose local workspace was most crowded Bennewitz et al [35] optimised

different possible priority schemes for teams of mobile robots Unfortunately

searching different sequences of priorities was computation-intensive and might fail to

find solutions to complex planning problems van den Berg and Overmars [43]

proposed a heuristic for assigning priorities to a team of robots in which a higher

priority was assigned to a robot with a longer moving distance Decoupled methods

often adopt priority-based approaches due to its prioritisation essence [35] They are

computationally simpler and can response faster in real-time applications in

comparison with coupled methods although they cannot guarantee optimal solutions

Moreover they are scalable for handling more mobile objects [32]

Based on the review above a dynamic priority-based decoupled method is proposed to

generate concurrent toolpaths for MMLM However MMLM has its distinct

characteristics with respect to multi-object motion planning First the tools do not have

self-control and sensing capabilities and they cannot communicate with each other

They are coordinated by a central controller Second the tools are normally

constrained to move along fixed paths of zigzags or spirals at constant deposition

speeds And third the toolpath planning approach for MMLM should take into account

the mechanical and thermal properties of the fabrication materials Hence the

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

4

via inkjet colour printing The print heads dispatched Al2O3 and ZrO2 aqueous

suspensions in different quantities to form a particular composition Malone et al [18]

developed the FabHome multi-material 3D printer for fabrication of

electro-mechanical systems Typical materials included polypropylene and ABS

thermoplastics and low melting-point metal alloys such as lead and tin A Zn-air cell

battery of about the size of a coin composed of five layers of different materials in a

plastic case was fabricated Objet Geometries Ltd [19] claimed that its Connex350

offered the ability to fabricate assemblies made of two types of photopolymer materials

with different mechanical properties The photopolymer materials were cured by

ultra-violet light immediately after jetting

These systems have made significant contributions to the development of MMLM

although they were mostly experimental and could only make simple prototypes of a

few types of materials However practical and viable MMLM systems for relatively

large complex objects have yet to be developed

It can be said that development of MMLM is mainly concerned with three major

research issues namely (1) fabrication materials (2) hardware mechanism for

deposition of materials and (3) computer software for planning the toolpaths and

subsequent process control of multiple tools for prototype fabrication These three

issues are generally studied by researchers of specialised expertise Nevertheless the

software issue of toolpath planning is particularly important as it has a significant

impact on the overall efficiency and quality of fabrication especially of large and

complex prototypes

13 Issues of Toolpath Planning

Toolpath planning for LM is mainly concerned with (i) contour filling strategy and (ii)

tool sequencing strategy [20] Contour filling strategy concerns mainly with how to

fill up the internal area of a contour This issue has been well-studied and standard

contour-filling patterns have been developed for LM [21] On the other hand tool

sequencing strategy is more about coordinating the motions of a set of tools each of

which deposits a material on specific contours to fabricate a multi-material prototype

safely and effectively Tool collisions and fabrication efficiency are main

considerations which may be exacerbated by the need to vary the tool deposition

5

speeds to suit different material properties and fabrication requirements [22] Tools

can be planned to deposit materials either sequentially to avoid collisions at the

expense of fabrication efficiency or concurrently to enhance fabrication efficiency

with risks of collisions This is a difficult problem of MMLM

Few research works on toolpath planning for MMLM have been reported Qiu et al

[12] developed a simulation system for toolpath analysis of MMLM In the system a

toolpath file per material was generated first and then integrated into one

multi-material toolpath file A toolpath planning method for two materials was reported

to reduce the defects and voids of a virtual part This method could process relatively

simple objects such as cylinder and cube Zhu and Yu [23] proposed a collision

detection and tool sequencing method for simple multi-material assemblies Zhou [24]

proposed a toolpath planning algorithm for fabrication of functionally graded

multi-material (FGM) objects First the gradual material distribution in each layer was

discretised into step-wise sub-regions in each of which the material could be assumed

homogeneous Then sequential toolpath for each sub-region was generated separately

The experimental MMLM systems described in the previous section also involved

some basic toolpath planning algorithms which were either sequential or could only

handle relatively simple prototypes Choi and Cheung [25] developed a multi-material

virtual prototyping system integrated with a topological hierarchy-based approach to

toolpath planning for MMLM This approach was later improved with an entire

envelope-based approach [20] and with a separate envelope-based approach [26]

These approaches were characterised by the construction of bounding envelopes

around slice contours by offsetting outward a distance of the tool radius Overlap test

was executed for these envelopes Tools in the non-overlapped envelopes could deposit

their specific materials concurrently without any collisions Nevertheless they did not

allow tools to move concurrently when the associated envelopes of the contours

overlapped incurring some idle time of tools

14 Research Objective

It can be concluded that toolpath planning for MMLM remains a vital but difficult

research issue which has yet to be fully tackled This paper therefore proposes a new

approach to concurrent toolpath planning for MMLM to further improve the

6

fabrication efficiency of relatively large complex prototypes This approach eradicates

the associated constraints of the previous approaches [20 25 26] to further improve

the fabrication efficiency It is characterised by construction of envelopes around

individual tools directly rather than around the slice contours of each layer Relative

tool positions are monitored to detect potential collisions at a predefined rate A

dynamic priority assignment scheme is applied to assign motion priorities of the tools

to avoid collisions and to coordinate the tool motions accordingly Deposition speeds

of tools can also be adjusted to suit different material properties and fabrication

requirements This concurrent toolpath planning approach can substantially shorten the

build-time of MMLM in comparison with the previous approaches

2 Related Works

21 Collision Detection

Tool collision is a major obstacle of multi-toolpath planning Collision detection also

known as interference detection or contact determination is an interdisciplinary issue

which is particularly important in motion planning robotics CADCAM etc [27]

Detection accuracy and computation cost are two inherently contradictory factors The

rate of collision detection is quite application-specific For instance haptic interfaces

require update rates of about one thousand hertz while about twenty to thirty updates

per second would be sufficient for real-time graphical applications [28] A number of

application-specific and practical collision detection algorithms have been proposed

and each of them has its own merits and deficiencies [29]

22 Multi-Object Motion Planning

In an MMLM process a number of tools deposit materials on specific contours to

fabricate a prototype preferably in concurrent motion to increase efficiency It can be

regarded as a more general control problem of multiple mobile objects sharing a

common workspace to complete their individual tasks without collision This problem

has received a great deal of attention in other applications such as mobile robots [30]

manipulation of robot arms [31] route planning for vehicles in a warehouse [32] etc

A variety of methods have been proposed to solve the multi-object motion planning

problem in which avoidance of collisions is paramount for safety and effectiveness In

7

general potential collisions are first detected and the object motions are subsequently

coordinated to avoid collisions and to improve optimality Optimisation objectives

include the minimisation of energy path length and motion time Indeed practicality

often demands a good balance between optimality (solution quality) and complexity

(computation cost) A broad review of multi-object motion planning can be found in

Lavalle‟s work [33] and this problem may be roughly categorised into coupled and

decoupled [34] as follows

221 Coupled Methods

A coupled method for multi-object motion planning combines the configuration spaces

of all the objects into a composite configuration space in which a feasible path is

searched for [32] In general it can achieve completeness and optimality However

the composite configuration space grows exponentially with the number of objects [35]

rendering the problem PSPACE-hard [36] Lavalle and Hutchinson [37] worked on

simultaneous optimisation of the motions of three robots from the start points to the

goals Li and Latombe [31] presented an approach to concurrent manipulation of two

robot arms to grab parts of various types on a conveyor and transfer them to their

respective goals while avoiding collisions with obstacles These works were among

early applications of coupled multi-object motion planning techniques on relatively

simple systems Indeed coupled methods are often used in systems with only a few

objects or for off-line applications

222 Decoupled Methods

In a decoupled method on the other hand the path of each object is separately

generated and subsequently coordinated to avoid collision [32] Different decoupled

methods have been applied to coordinate the motion of multiple objects including

adjustment of geometric paths modification of velocities and time delay [34] Wagner

et al [30] demonstrated an efficient approach to coordinating a group of cooperative

cleaner robots to clean a common dirty floor Lee and Kim [38] developed a

multi-robot printing system in which the host computer commanded a set of client

printer-robots to cooperatively draw a picture on a sheet of paper In the work of Peng

and Akella [39] the path of each robot was first generated irrespective of other robots

while the velocities were subsequently altered along their paths to avoid collision

Rekleitis et al [40] presented an algorithm to control a team of robots moving in

8

zigzags to complete the coverage of a 2D plane Lee et al [41] used potential

functions to guide objects to their destinations Chang et al [42] used a time delay

method to avoid collisions between two robot arms The minimum delay time needed

for collision avoidance was obtained by a collision map scheme

In essence decoupled methods involve assigning priorities to objects to determine the

order in which the paths are to be coordinated [43] Erdmann and Perez [44] assigned

static priority to each robot and sequentially computed paths in a time-varying

configuration space Ferrari et al [45] used a fixed priority scheme and chose random

detours for the robots with lower priorities These static priority schemes were suitable

for predefined applications On the other hand dynamic priority schemes are more

flexible to handle different situations Azarm and Schmidt [46] proposed an approach

that considered all possible priority assignments for up to three robots Clark et al [47]

presented a motion planning system that could construct collision-free paths for groups

of robots in dynamic environments They introduced a priority scheme that gave way

to the robot whose local workspace was most crowded Bennewitz et al [35] optimised

different possible priority schemes for teams of mobile robots Unfortunately

searching different sequences of priorities was computation-intensive and might fail to

find solutions to complex planning problems van den Berg and Overmars [43]

proposed a heuristic for assigning priorities to a team of robots in which a higher

priority was assigned to a robot with a longer moving distance Decoupled methods

often adopt priority-based approaches due to its prioritisation essence [35] They are

computationally simpler and can response faster in real-time applications in

comparison with coupled methods although they cannot guarantee optimal solutions

Moreover they are scalable for handling more mobile objects [32]

Based on the review above a dynamic priority-based decoupled method is proposed to

generate concurrent toolpaths for MMLM However MMLM has its distinct

characteristics with respect to multi-object motion planning First the tools do not have

self-control and sensing capabilities and they cannot communicate with each other

They are coordinated by a central controller Second the tools are normally

constrained to move along fixed paths of zigzags or spirals at constant deposition

speeds And third the toolpath planning approach for MMLM should take into account

the mechanical and thermal properties of the fabrication materials Hence the

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

5

speeds to suit different material properties and fabrication requirements [22] Tools

can be planned to deposit materials either sequentially to avoid collisions at the

expense of fabrication efficiency or concurrently to enhance fabrication efficiency

with risks of collisions This is a difficult problem of MMLM

Few research works on toolpath planning for MMLM have been reported Qiu et al

[12] developed a simulation system for toolpath analysis of MMLM In the system a

toolpath file per material was generated first and then integrated into one

multi-material toolpath file A toolpath planning method for two materials was reported

to reduce the defects and voids of a virtual part This method could process relatively

simple objects such as cylinder and cube Zhu and Yu [23] proposed a collision

detection and tool sequencing method for simple multi-material assemblies Zhou [24]

proposed a toolpath planning algorithm for fabrication of functionally graded

multi-material (FGM) objects First the gradual material distribution in each layer was

discretised into step-wise sub-regions in each of which the material could be assumed

homogeneous Then sequential toolpath for each sub-region was generated separately

The experimental MMLM systems described in the previous section also involved

some basic toolpath planning algorithms which were either sequential or could only

handle relatively simple prototypes Choi and Cheung [25] developed a multi-material

virtual prototyping system integrated with a topological hierarchy-based approach to

toolpath planning for MMLM This approach was later improved with an entire

envelope-based approach [20] and with a separate envelope-based approach [26]

These approaches were characterised by the construction of bounding envelopes

around slice contours by offsetting outward a distance of the tool radius Overlap test

was executed for these envelopes Tools in the non-overlapped envelopes could deposit

their specific materials concurrently without any collisions Nevertheless they did not

allow tools to move concurrently when the associated envelopes of the contours

overlapped incurring some idle time of tools

14 Research Objective

It can be concluded that toolpath planning for MMLM remains a vital but difficult

research issue which has yet to be fully tackled This paper therefore proposes a new

approach to concurrent toolpath planning for MMLM to further improve the

6

fabrication efficiency of relatively large complex prototypes This approach eradicates

the associated constraints of the previous approaches [20 25 26] to further improve

the fabrication efficiency It is characterised by construction of envelopes around

individual tools directly rather than around the slice contours of each layer Relative

tool positions are monitored to detect potential collisions at a predefined rate A

dynamic priority assignment scheme is applied to assign motion priorities of the tools

to avoid collisions and to coordinate the tool motions accordingly Deposition speeds

of tools can also be adjusted to suit different material properties and fabrication

requirements This concurrent toolpath planning approach can substantially shorten the

build-time of MMLM in comparison with the previous approaches

2 Related Works

21 Collision Detection

Tool collision is a major obstacle of multi-toolpath planning Collision detection also

known as interference detection or contact determination is an interdisciplinary issue

which is particularly important in motion planning robotics CADCAM etc [27]

Detection accuracy and computation cost are two inherently contradictory factors The

rate of collision detection is quite application-specific For instance haptic interfaces

require update rates of about one thousand hertz while about twenty to thirty updates

per second would be sufficient for real-time graphical applications [28] A number of

application-specific and practical collision detection algorithms have been proposed

and each of them has its own merits and deficiencies [29]

22 Multi-Object Motion Planning

In an MMLM process a number of tools deposit materials on specific contours to

fabricate a prototype preferably in concurrent motion to increase efficiency It can be

regarded as a more general control problem of multiple mobile objects sharing a

common workspace to complete their individual tasks without collision This problem

has received a great deal of attention in other applications such as mobile robots [30]

manipulation of robot arms [31] route planning for vehicles in a warehouse [32] etc

A variety of methods have been proposed to solve the multi-object motion planning

problem in which avoidance of collisions is paramount for safety and effectiveness In

7

general potential collisions are first detected and the object motions are subsequently

coordinated to avoid collisions and to improve optimality Optimisation objectives

include the minimisation of energy path length and motion time Indeed practicality

often demands a good balance between optimality (solution quality) and complexity

(computation cost) A broad review of multi-object motion planning can be found in

Lavalle‟s work [33] and this problem may be roughly categorised into coupled and

decoupled [34] as follows

221 Coupled Methods

A coupled method for multi-object motion planning combines the configuration spaces

of all the objects into a composite configuration space in which a feasible path is

searched for [32] In general it can achieve completeness and optimality However

the composite configuration space grows exponentially with the number of objects [35]

rendering the problem PSPACE-hard [36] Lavalle and Hutchinson [37] worked on

simultaneous optimisation of the motions of three robots from the start points to the

goals Li and Latombe [31] presented an approach to concurrent manipulation of two

robot arms to grab parts of various types on a conveyor and transfer them to their

respective goals while avoiding collisions with obstacles These works were among

early applications of coupled multi-object motion planning techniques on relatively

simple systems Indeed coupled methods are often used in systems with only a few

objects or for off-line applications

222 Decoupled Methods

In a decoupled method on the other hand the path of each object is separately

generated and subsequently coordinated to avoid collision [32] Different decoupled

methods have been applied to coordinate the motion of multiple objects including

adjustment of geometric paths modification of velocities and time delay [34] Wagner

et al [30] demonstrated an efficient approach to coordinating a group of cooperative

cleaner robots to clean a common dirty floor Lee and Kim [38] developed a

multi-robot printing system in which the host computer commanded a set of client

printer-robots to cooperatively draw a picture on a sheet of paper In the work of Peng

and Akella [39] the path of each robot was first generated irrespective of other robots

while the velocities were subsequently altered along their paths to avoid collision

Rekleitis et al [40] presented an algorithm to control a team of robots moving in

8

zigzags to complete the coverage of a 2D plane Lee et al [41] used potential

functions to guide objects to their destinations Chang et al [42] used a time delay

method to avoid collisions between two robot arms The minimum delay time needed

for collision avoidance was obtained by a collision map scheme

In essence decoupled methods involve assigning priorities to objects to determine the

order in which the paths are to be coordinated [43] Erdmann and Perez [44] assigned

static priority to each robot and sequentially computed paths in a time-varying

configuration space Ferrari et al [45] used a fixed priority scheme and chose random

detours for the robots with lower priorities These static priority schemes were suitable

for predefined applications On the other hand dynamic priority schemes are more

flexible to handle different situations Azarm and Schmidt [46] proposed an approach

that considered all possible priority assignments for up to three robots Clark et al [47]

presented a motion planning system that could construct collision-free paths for groups

of robots in dynamic environments They introduced a priority scheme that gave way

to the robot whose local workspace was most crowded Bennewitz et al [35] optimised

different possible priority schemes for teams of mobile robots Unfortunately

searching different sequences of priorities was computation-intensive and might fail to

find solutions to complex planning problems van den Berg and Overmars [43]

proposed a heuristic for assigning priorities to a team of robots in which a higher

priority was assigned to a robot with a longer moving distance Decoupled methods

often adopt priority-based approaches due to its prioritisation essence [35] They are

computationally simpler and can response faster in real-time applications in

comparison with coupled methods although they cannot guarantee optimal solutions

Moreover they are scalable for handling more mobile objects [32]

Based on the review above a dynamic priority-based decoupled method is proposed to

generate concurrent toolpaths for MMLM However MMLM has its distinct

characteristics with respect to multi-object motion planning First the tools do not have

self-control and sensing capabilities and they cannot communicate with each other

They are coordinated by a central controller Second the tools are normally

constrained to move along fixed paths of zigzags or spirals at constant deposition

speeds And third the toolpath planning approach for MMLM should take into account

the mechanical and thermal properties of the fabrication materials Hence the

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

6

fabrication efficiency of relatively large complex prototypes This approach eradicates

the associated constraints of the previous approaches [20 25 26] to further improve

the fabrication efficiency It is characterised by construction of envelopes around

individual tools directly rather than around the slice contours of each layer Relative

tool positions are monitored to detect potential collisions at a predefined rate A

dynamic priority assignment scheme is applied to assign motion priorities of the tools

to avoid collisions and to coordinate the tool motions accordingly Deposition speeds

of tools can also be adjusted to suit different material properties and fabrication

requirements This concurrent toolpath planning approach can substantially shorten the

build-time of MMLM in comparison with the previous approaches

2 Related Works

21 Collision Detection

Tool collision is a major obstacle of multi-toolpath planning Collision detection also

known as interference detection or contact determination is an interdisciplinary issue

which is particularly important in motion planning robotics CADCAM etc [27]

Detection accuracy and computation cost are two inherently contradictory factors The

rate of collision detection is quite application-specific For instance haptic interfaces

require update rates of about one thousand hertz while about twenty to thirty updates

per second would be sufficient for real-time graphical applications [28] A number of

application-specific and practical collision detection algorithms have been proposed

and each of them has its own merits and deficiencies [29]

22 Multi-Object Motion Planning

In an MMLM process a number of tools deposit materials on specific contours to

fabricate a prototype preferably in concurrent motion to increase efficiency It can be

regarded as a more general control problem of multiple mobile objects sharing a

common workspace to complete their individual tasks without collision This problem

has received a great deal of attention in other applications such as mobile robots [30]

manipulation of robot arms [31] route planning for vehicles in a warehouse [32] etc

A variety of methods have been proposed to solve the multi-object motion planning

problem in which avoidance of collisions is paramount for safety and effectiveness In

7

general potential collisions are first detected and the object motions are subsequently

coordinated to avoid collisions and to improve optimality Optimisation objectives

include the minimisation of energy path length and motion time Indeed practicality

often demands a good balance between optimality (solution quality) and complexity

(computation cost) A broad review of multi-object motion planning can be found in

Lavalle‟s work [33] and this problem may be roughly categorised into coupled and

decoupled [34] as follows

221 Coupled Methods

A coupled method for multi-object motion planning combines the configuration spaces

of all the objects into a composite configuration space in which a feasible path is

searched for [32] In general it can achieve completeness and optimality However

the composite configuration space grows exponentially with the number of objects [35]

rendering the problem PSPACE-hard [36] Lavalle and Hutchinson [37] worked on

simultaneous optimisation of the motions of three robots from the start points to the

goals Li and Latombe [31] presented an approach to concurrent manipulation of two

robot arms to grab parts of various types on a conveyor and transfer them to their

respective goals while avoiding collisions with obstacles These works were among

early applications of coupled multi-object motion planning techniques on relatively

simple systems Indeed coupled methods are often used in systems with only a few

objects or for off-line applications

222 Decoupled Methods

In a decoupled method on the other hand the path of each object is separately

generated and subsequently coordinated to avoid collision [32] Different decoupled

methods have been applied to coordinate the motion of multiple objects including

adjustment of geometric paths modification of velocities and time delay [34] Wagner

et al [30] demonstrated an efficient approach to coordinating a group of cooperative

cleaner robots to clean a common dirty floor Lee and Kim [38] developed a

multi-robot printing system in which the host computer commanded a set of client

printer-robots to cooperatively draw a picture on a sheet of paper In the work of Peng

and Akella [39] the path of each robot was first generated irrespective of other robots

while the velocities were subsequently altered along their paths to avoid collision

Rekleitis et al [40] presented an algorithm to control a team of robots moving in

8

zigzags to complete the coverage of a 2D plane Lee et al [41] used potential

functions to guide objects to their destinations Chang et al [42] used a time delay

method to avoid collisions between two robot arms The minimum delay time needed

for collision avoidance was obtained by a collision map scheme

In essence decoupled methods involve assigning priorities to objects to determine the

order in which the paths are to be coordinated [43] Erdmann and Perez [44] assigned

static priority to each robot and sequentially computed paths in a time-varying

configuration space Ferrari et al [45] used a fixed priority scheme and chose random

detours for the robots with lower priorities These static priority schemes were suitable

for predefined applications On the other hand dynamic priority schemes are more

flexible to handle different situations Azarm and Schmidt [46] proposed an approach

that considered all possible priority assignments for up to three robots Clark et al [47]

presented a motion planning system that could construct collision-free paths for groups

of robots in dynamic environments They introduced a priority scheme that gave way

to the robot whose local workspace was most crowded Bennewitz et al [35] optimised

different possible priority schemes for teams of mobile robots Unfortunately

searching different sequences of priorities was computation-intensive and might fail to

find solutions to complex planning problems van den Berg and Overmars [43]

proposed a heuristic for assigning priorities to a team of robots in which a higher

priority was assigned to a robot with a longer moving distance Decoupled methods

often adopt priority-based approaches due to its prioritisation essence [35] They are

computationally simpler and can response faster in real-time applications in

comparison with coupled methods although they cannot guarantee optimal solutions

Moreover they are scalable for handling more mobile objects [32]

Based on the review above a dynamic priority-based decoupled method is proposed to

generate concurrent toolpaths for MMLM However MMLM has its distinct

characteristics with respect to multi-object motion planning First the tools do not have

self-control and sensing capabilities and they cannot communicate with each other

They are coordinated by a central controller Second the tools are normally

constrained to move along fixed paths of zigzags or spirals at constant deposition

speeds And third the toolpath planning approach for MMLM should take into account

the mechanical and thermal properties of the fabrication materials Hence the

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

7

general potential collisions are first detected and the object motions are subsequently

coordinated to avoid collisions and to improve optimality Optimisation objectives

include the minimisation of energy path length and motion time Indeed practicality

often demands a good balance between optimality (solution quality) and complexity

(computation cost) A broad review of multi-object motion planning can be found in

Lavalle‟s work [33] and this problem may be roughly categorised into coupled and

decoupled [34] as follows

221 Coupled Methods

A coupled method for multi-object motion planning combines the configuration spaces

of all the objects into a composite configuration space in which a feasible path is

searched for [32] In general it can achieve completeness and optimality However

the composite configuration space grows exponentially with the number of objects [35]

rendering the problem PSPACE-hard [36] Lavalle and Hutchinson [37] worked on

simultaneous optimisation of the motions of three robots from the start points to the

goals Li and Latombe [31] presented an approach to concurrent manipulation of two

robot arms to grab parts of various types on a conveyor and transfer them to their

respective goals while avoiding collisions with obstacles These works were among

early applications of coupled multi-object motion planning techniques on relatively

simple systems Indeed coupled methods are often used in systems with only a few

objects or for off-line applications

222 Decoupled Methods

In a decoupled method on the other hand the path of each object is separately

generated and subsequently coordinated to avoid collision [32] Different decoupled

methods have been applied to coordinate the motion of multiple objects including

adjustment of geometric paths modification of velocities and time delay [34] Wagner

et al [30] demonstrated an efficient approach to coordinating a group of cooperative

cleaner robots to clean a common dirty floor Lee and Kim [38] developed a

multi-robot printing system in which the host computer commanded a set of client

printer-robots to cooperatively draw a picture on a sheet of paper In the work of Peng

and Akella [39] the path of each robot was first generated irrespective of other robots

while the velocities were subsequently altered along their paths to avoid collision

Rekleitis et al [40] presented an algorithm to control a team of robots moving in

8

zigzags to complete the coverage of a 2D plane Lee et al [41] used potential

functions to guide objects to their destinations Chang et al [42] used a time delay

method to avoid collisions between two robot arms The minimum delay time needed

for collision avoidance was obtained by a collision map scheme

In essence decoupled methods involve assigning priorities to objects to determine the

order in which the paths are to be coordinated [43] Erdmann and Perez [44] assigned

static priority to each robot and sequentially computed paths in a time-varying

configuration space Ferrari et al [45] used a fixed priority scheme and chose random

detours for the robots with lower priorities These static priority schemes were suitable

for predefined applications On the other hand dynamic priority schemes are more

flexible to handle different situations Azarm and Schmidt [46] proposed an approach

that considered all possible priority assignments for up to three robots Clark et al [47]

presented a motion planning system that could construct collision-free paths for groups

of robots in dynamic environments They introduced a priority scheme that gave way

to the robot whose local workspace was most crowded Bennewitz et al [35] optimised

different possible priority schemes for teams of mobile robots Unfortunately

searching different sequences of priorities was computation-intensive and might fail to

find solutions to complex planning problems van den Berg and Overmars [43]

proposed a heuristic for assigning priorities to a team of robots in which a higher

priority was assigned to a robot with a longer moving distance Decoupled methods

often adopt priority-based approaches due to its prioritisation essence [35] They are

computationally simpler and can response faster in real-time applications in

comparison with coupled methods although they cannot guarantee optimal solutions

Moreover they are scalable for handling more mobile objects [32]

Based on the review above a dynamic priority-based decoupled method is proposed to

generate concurrent toolpaths for MMLM However MMLM has its distinct

characteristics with respect to multi-object motion planning First the tools do not have

self-control and sensing capabilities and they cannot communicate with each other

They are coordinated by a central controller Second the tools are normally

constrained to move along fixed paths of zigzags or spirals at constant deposition

speeds And third the toolpath planning approach for MMLM should take into account

the mechanical and thermal properties of the fabrication materials Hence the

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

8

zigzags to complete the coverage of a 2D plane Lee et al [41] used potential

functions to guide objects to their destinations Chang et al [42] used a time delay

method to avoid collisions between two robot arms The minimum delay time needed

for collision avoidance was obtained by a collision map scheme

In essence decoupled methods involve assigning priorities to objects to determine the

order in which the paths are to be coordinated [43] Erdmann and Perez [44] assigned

static priority to each robot and sequentially computed paths in a time-varying

configuration space Ferrari et al [45] used a fixed priority scheme and chose random

detours for the robots with lower priorities These static priority schemes were suitable

for predefined applications On the other hand dynamic priority schemes are more

flexible to handle different situations Azarm and Schmidt [46] proposed an approach

that considered all possible priority assignments for up to three robots Clark et al [47]

presented a motion planning system that could construct collision-free paths for groups

of robots in dynamic environments They introduced a priority scheme that gave way

to the robot whose local workspace was most crowded Bennewitz et al [35] optimised

different possible priority schemes for teams of mobile robots Unfortunately

searching different sequences of priorities was computation-intensive and might fail to

find solutions to complex planning problems van den Berg and Overmars [43]

proposed a heuristic for assigning priorities to a team of robots in which a higher

priority was assigned to a robot with a longer moving distance Decoupled methods

often adopt priority-based approaches due to its prioritisation essence [35] They are

computationally simpler and can response faster in real-time applications in

comparison with coupled methods although they cannot guarantee optimal solutions

Moreover they are scalable for handling more mobile objects [32]

Based on the review above a dynamic priority-based decoupled method is proposed to

generate concurrent toolpaths for MMLM However MMLM has its distinct

characteristics with respect to multi-object motion planning First the tools do not have

self-control and sensing capabilities and they cannot communicate with each other

They are coordinated by a central controller Second the tools are normally

constrained to move along fixed paths of zigzags or spirals at constant deposition

speeds And third the toolpath planning approach for MMLM should take into account

the mechanical and thermal properties of the fabrication materials Hence the

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

9

multi-object motion planning technique has to be suitably adapted for concurrent

toolpath planning for MMLM

3 The Dynamic Priority-based Approach to Concurrent Toolpath

Planning for MMLM

In a general scenario of multi-objects the object motions may be omni-directional and

erratic with multiple intersections as shown in Figure 1 But tools in MMLM are

normally constrained to move along fixed paths of zigzags or spirals at constant

deposition speeds inside specific contours that do not overlap as shown in Figure 2

The material deposition mechanism of MMLM may consist of a set of tools each of

which deposits a specific material on the related slice contours The tools do not invade

other unrelated contours and there may be collisions of tools only when they get in

close vicinity like the purple tool and the yellow tool Indeed some hardware

constraints may hinder concurrent deposition of materials and consideration of

collisions between tools and support mechanisms in addition to tool collisions would

further complicate the control problem But as pointed out previously hardware

mechanism is another research issue of MMLM We therefore assume appropriate

deposition hardware without tool-support interferences would be available and we

limit the scope of this paper to consider collisions between tools only

Figure 1 A general motion scenario of multiple objects

start

goal

Model of a human

eye ball in skull

Y

Figure 2 Schematic of the proposed MMLM mechanism

O

Slice

Skull

Skull

X

Eye ball

Potential collision

Hatch lines (toolpaths)

in zigzags

A layer to be deposited of

six materials with six tools

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

10

The proposed concurrent toolpath planning approach first generates the toolpath (hatch

lines) of each tool for depositing a specific material on the related contours of a layer

The tools are then coordinated to fabricate the layer concurrently Collision detection

of tools is executed at a predefined rate When a potential collision between a pair of

tools is detected their traverse speeds along the x-axis are compared and a higher

priority is assigned to the tool travelling at a higher traverse speed The tool with a

higher priority continues to deposit material along its original path while the one with

a lower priority gives way by pausing at a suitable point until the potential collision is

eliminated As such the level of concurrent tool motions and hence the overall

fabrication efficiency can be significantly improved Moreover the deposition speeds

of tools can be adjusted to suit different material properties and fabrication

requirements The following sections present the details of traverse speed collision

detection and motion priority assignment for implementation of the proposed

concurrent toolpath planning approach

31 Analysis of Traverse Speed Vx

There are two common modes in which a tool fills up a contour (1) the zigzag mode

where the toolpaths are hatch lines which can be either horizontal or at 45deg slope or

vertical [12] and (2) the spiral mode where the toolpaths are offset inwards from the

contours The proposed approach adopts the zigzag mode with vertical hatch lines As

shown in Figure 3(a) a tool moves in up-and-down zigzags at deposition speed V to

deposit material to fill up a circular contour As a whole the tool moves from the left to

the right at a traverse speed Vx The deposition speed V is bidirectional while the

traverse speed Vx is unidirectional V can be varied to suit different material properties

and fabrication requirements but it is constant for a specific material during the whole

fabrication process of a prototype Vx on the other hand depends on the hatch lines

Figure 3(b) shows the lengths and the widths of two adjacent hatch lines While the

width w remains constant the length h varies across the contours during the fabrication

process Assume that a tool traverses a distance of the hatch width w along the x-axis in

a time it takes to complete depositing material along the hatch length h The time that

a tool spends on a hatch line is T = hV and therefore the tool‟s traverse speed is given

by Vx = wT = wVh It can be seen in Figure 3(a) that the hatch length increases from

the leftmost to the centre of the circle and decreases from the centre to the rightmost of

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

11

the circle afterwards Accordingly the traverse speed Vx of a tool decreases first and

increases afterwards The curve of tool displacement along X-axis versus time is

shown in the X-t graph in Figure 3(c) whose varying gradient is Vx

It can be said that the traverse speed Vx of a tool is instantaneous varying across a

contour during the fabrication process Motion priorities are dynamically assigned to

the tools according to their traverse speeds to avoid collisions

32 Collision Detection

Collision detection plays an important role in avoiding collisions to ensure the safety

and effectiveness of an MMLM process Since the tools deposit specific materials at

related slice contours concurrently there may be collisions between a pair of tools

when they get in close vicinity In multi-object planning object motions may be

omni-directional and erratic with multiple intersections rendering the relative

velocities and the motion directions of objects complex factors in collision detection It

(c) X-t graph of the circular contour

A hatch line (toolpath) indicating the

direction of tool motion

Strip of solid (voxel)

(b) Hatch length and hatch width

Layer

thickness

(hatch width)

h (hatch length)

w

D

w

Y

e

s

Y

X

Z

O

Figure 3 Analysis of traverse speed

Hatch line (Toolpath)

V

O X

Y

(a) A simple layer of a circular contour

Vx

Tool

Contour

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

12

may be necessary to iterate detection of the instantaneous relative velocities and centre

distances of tools which is computationally intensive if the detection rate is high

However as we adopt up-and-down zigzags as the contour filling strategy detection of

tool collisions for MMLM can be simplified considerably It would only be necessary

to consider the distance between the ends of the hatch lines being deposited by the

tools in question In general collisions between a pair of tools would not happen if

either the horizontal or the vertical distance between the ends of two hatch lines is

greater than the sum of the tool radii regardless of the deposition speeds and directions

of the tools Hence collision detection is only needed at a predefined rate of the

completion of a number of hatch lines making the algorithm relatively simple yet

effective The principle of the proposed collision detection is outlined as follows

A cylinder is constructed around each tool as the bounding envelope and hence a circle

projected on the X-Y plane represents a tool In Figure 4(a) a red tool and a blue tool

are depositing materials along hatch lines AB and CD respectively The tools are of

the same radius R Let dx be the horizontal distance between the ends of two hatch

lines which are currently being deposited by the associated tools respectively and dy

the closest vertical distance between the ends of the two hatch lines Since dx lt 2R

and dy lt 2R the tools are about to collide when the red tool is near point B and the

blue tool is close to C

Condition of potential collision

Any two tools moving along their respective hatch lines are considered as about to

collide if the following condition holds

dx le 2R+safety margin = 2R+R=3R AND dy le 2R

The proposed algorithm incorporates a safety margin of R in the x-axis direction

which may be changed if necessary for further safeguard against potential collisions as

shown in Figure 4(b) Figures 4(c) and 4(d) show two cases in which the tools would

not collide when dx gt 3R and when dx lt 3R but dy gt 2R respectively

The rate of collision detection should be well chosen to strike a good balance between

detection accuracy and computation cost A high detection rate improves accuracy with

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

13

more computation resources while a low detection rate reduces computation cost at the

expense of accuracy For the MMLM process the highest rate is to detect collision

after fabrication of a hatch line On the other hand we adopt the lowest allowable rate

of collision detection which is derived as follows In Figure 4(b) imagine an extreme

situation in which the traverse speed VxB of the blue tool approaches zero the red tool

will catch up with the blue tool after the completion of n = Rw hatch lines where R is

the safety margin and w is the hatch width Hence an interval of n hatch lines is the

lowest allowable rate of collision detection Whenever a tool first completes n hatch

lines the collision detection is executed

X

(a) Tools likely to collide

Y

O

dy lt 2R

dx lt 2R

A

B

VR

VB

C

D

VxR

VxB

X

(b) Safety margin

Y

O

A

B

VR

VB

C

D

R safety margin

VxR

VxB

Figure 4 Tool collision detection for MMLM

dx gt3R

X O

(c) Tools not likely to collide

Y VxR

VB

VR

VxB

dy gt2R dxlt3R

X O

Y

(d) Tools not likely to collide

VR VxR

VB VxB

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

14

33 Dynamic Assignment of Priorities for Tool Motion Coordination

When potential collision between a pair of tools is detected a higher motion priority is

assigned to the tool that travels at a higher traverse speed for it to continue to deposit

material along its original path The tool with a lower priority gives way by waiting at

a suitable point until the potential collision is eliminated This priority scheme ensures

a potential collision is resolved as quickly as possible so that the paused tool can

resume fabrication to minimise uneven cooling that may impair the prototype quality

The procedure of dynamic assignment of tool motion priorities is as follows

Step 1 Read in a new layer initialise the speeds of tools and start fabrication

Step 2 Perform collision detection between all pairs of the tools

Step 3 If no potential collision is detected go to Step 8

Step 4 Find the pair of tools which is likely to collide

Step 5 Calculate the traverse speeds Vx = wVh of tools which are likely to collide

Step 6 Assign priorities to the tools according to their traverse speeds A higher

priority is assigned to a tool at a higher Vx

Step 7 A tool with a higher priority continues deposition along its original path

while the one with a lower priority waits at a suitable point to give way until

the potential collision is eliminated

Step 8 Tools without potential collision deposit materials concurrently

Step 9 If a layer is not completed repeat from Step 2 Otherwise repeat from Step 1

until all the layers are completed

34 A Simple Prototype to Illustrate the Proposed Approach

The following section illustrates how the proposed dynamic priority-based approach to

concurrent toolpath planning for MMLM works

341 Workflow of the Proposed Concurrent Toolpath Planning Approach

Figure 5 shows a simple prototype of dimensions 230mm x 100m x 6mm to be made

of three discrete materials The prototype is sliced into 30 layers In Figure 6 three

tools Tred Tgreen and Tblue of the same radius R=10mm deposit the red green and

blue materials respectively on a selected layer For simplicity the deposition speeds of

the three tools are set to be VR＝VB＝VG＝10mms-1

and the hatch width w is 1mm

The effect of adjusting the deposition speeds will be presented in the next section

Figure 5 A simple prototype of three discrete materials

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

15

To start fabricating this layer the three tools are initialised with their deposition speeds

and they move from their datum positions around O to the bottom point of the leftmost

hatch line of their respective contours The proposed collision detection algorithm is

executed on all pairs of the tools At first there is no potential collision as dx between

all pairs of current hatch lines are greater than 3R so all the three tools can start to

deposit specific materials concurrently The traverse speed of each tool is VxR = VxG =

VxB = wVh where w and h are the width and length of the current hatch line being

deposited by each tool

As shown in Figure 6 the length of each red hatch line is at first shorter than that of the

blue one the traverse speed of the red tool is thus higher than that of the blue one ie

VxR gt VxB The red tool will catch up with the blue one some time later As shown in

Figure 7 collision detection indicates that there is a potential collision between the red

tool and the blue tool at time t1 because the condition of dx lt3R and dy lt2R holds The

dynamic priority assignment algorithm is executed here to adjust the motion priorities

of the red tool and the blue tool accordingly It calculates and compares the traverse

speeds of the tools at their respective current hatch lines and assigns priorities to these

tools according to their traverse speeds Here a higher priority is assigned to the red

tool for it is at a higher traverse speed The red tool continues its original path while

Figure 6 Three tools fabricating the selected layer

VR VxR

X

Y

O

VG VxG

VB

VxB

tool at time t1

tool at time t2

Start position of Tgreen

Start position of Tred

Start position

of Tblue

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

16

the blue tool with a lower priority waits at a suitable point to give way until the

potential collision is eliminated As to the blue tool waiting at a suitable point means

that the blue tool waits at the far end of its current hatch line after completing

deposition (shown as the solid blue circle in Figure 6) in order not to hamper the

quality of the resulting prototype

Now while the blue tool is paused the red tool and the green tool deposit materials

concurrently because no potential collision between them is detected Some time after

t1 the collision detection algorithm finds that the potential collision between the red

tool and the blue tool has been eliminated Subsequently all the three tools are

commanded to fabricate concurrently

Some time after the tools gradually traverse to the right side of the respective contours

the length of the blue hatch line becomes shorter than that of the red one Thus the

traverse speed of the blue tool becomes higher than that of the red tool and the blue

tool is catching up with the red tool At time t2 as shown in dashed circles in Figure 6

and time t2 in Figure 7 collision detection finds that there is a potential collision

between the red tool and the blue tool again

Now the traverse speed of the blue tool overtakes that of the red tool The priorities of

these two tools are reversed ie a higher priority is assigned to the blue tool Thus the

blue tool continues its original path while the red tool with a lower priority waits at a

suitable point to give way until the potential collision is eliminated At this moment

Figure 7 X-t graph of the selected layer

t1 t2

Potential collision detected

dynamic priority assignment

executed

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

17

the blue tool and the green tool without potential collision deposit concurrently while

the red tool is waiting Some time after t2 the collision detection algorithm finds that

the potential collision between the red tool and the blue tool has been eliminated All

the three tools can again fabricate concurrently until the layer is completed Digital

fabrication of the selected layer with VR =VB=VG =10mms-1

is shown from Figure 8(a)

to Figure 8(e)

342 Adjustment of Deposition Speeds

To suit different material properties and fabrication requirements it may be necessary

to adjust the deposition speed of a tool In this section the deposition speeds of the

red green and blue tools are varied to be VR =15mms-1

VG =10mms-1

VB =8mms-1

Figure 8 Digital fabrication of the selected layer

(c) Three tools move concurrently

Tred

(a) Three tools move concurrently (b) Blue tool waits Red tool and green

tool move concurrently

(d) Red tool waits Blue tool and

green tool move concurrently

(e) Three tools move concurrently to

complete the layer

Tblue

Tgreen Tred

Tblue

Tgreen

Tred

Tblue Tgreen

Tred

Tblue

Tgreen

Tred

Tblue

Tgreen

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

18

respectively Figure 9 shows the X-t graph with these adjusted deposition speeds

Like in the previous example the three tools first move concurrently to deposit their

specific materials as shown in Figure 10(a) Then due to the higher deposition speed

of the red tool and the shorter length of red hatch lines the traverse speed of the red

tool is much higher than that of the blue one Hence the red tool will quickly catch up

with the blue one at time t1 as shown the X-t graph in Figure 9 The dynamic priority

assignment algorithm is executed for the red tool and the blue tool accordingly A

higher priority is assigned to the red tool which is at a higher traverse speed The red

Figure 9 X-t graph of the selected layer with adjusted deposition speeds

t1

Potential collision detected

dynamic priority assignment

executed

Figure 10 Digital fabrication of the selected layer at adjusted deposition speeds

(c) Three tools deposit materials

concurrently to complete the layer

Tred

Tgreen

Tblue

(a) Three tools deposit materials

concurrently

(b) Blue tool waits while red tool and green

tool deposit materials concurrently

Tred

Tblue

Tgreen Tred

Tblue

Tgreen

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

19

tool continues fabrication along its original path while the blue tool with a lower

priority waits at a suitable point to give way until the potential collision is eliminated

as shown in Figure 10(b)

Now the red tool and the green tool which are not likely to collide deposit materials

concurrently while the blue tool is waiting Some time after t1 the collision detection

algorithm finds that the potential collision between the red tool and the blue tool has

been eliminated The three tools can again deposit materials concurrently as shown in

Figure 10(c) Hence in comparison with the previous example of uniform deposition

speed the red tool travels a lot faster and it will never be caught up with by the blue

tool after t1 All the three tools continue to deposit materials concurrently until the layer

is completed

4 Implementation and Case Studies

The proposed dynamic priority-based approach has been incorporated with other major

in-house modules for STL model manipulation slicing hierarchical contour sorting

contour hatching and digital fabrication to form an integrated system for

multi-material virtual prototyping (MMVP) [48] The system was implemented in

CC++ and integrated with WorldToolKit Release 9 for fabrication simulation in a

semi-immersive virtual reality (VR) environment and with Virtools Dev toolkits for a

full-immersive CAVE VR environment It can digitally fabricate relatively complex

objects for biomedical applications and advanced product development The following

presents two case studies a human ear model and a toy tank to demonstrate some

possible applications of the MMVP system and to verify the effectiveness of the

proposed dynamic priority-based approach to concurrent toolpath planning for

MMLM

41 A Human Ear Model

In recent years doctors and surgeons have often used biomedical prototypes to help

visualise the anatomy of human organs and design prostheses for surgical planning and

implantations Indeed multi-material prototypes would be particularly useful for study

and planning of delicate surgeries in that they can differentiate clearly one part from

another or tissues from blood vessels of a human organ A model of a human ear

with dimensions of 175mm x 186mm x 190mm as shown in Figure 11 is sliced into

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

20

800 layers with layer thickness of 02mm Figure 12 shows the contours of a layer to

be made of four materials coloured in orange pink blue and grey with four tools of

the same radius R=10mm

The deposition speeds are set to be VP =20mms-1

VO =15mms-1

VB =5mms-1

and

VG=5mms-1

for the tools that deposit pink orange blue and grey materials

respectively Adjusted deposition speeds will be presented later

Figure 11 Anatomical model of a human ear

Slicing

plane

Auricular

Skull Tympanum Auditory nerve

Inner ear

Middle ear Styloid

process

Y

X O

Figure 12 A selected layer of the human ear model

VP VxP

VO

Grey tool to deposit

this contour

Blue tool to deposit

this contour

VxO tool at time t1

tool at time t2

21

At first the pink orange blue and grey tools move concurrently to deposit their

specific materials When t = t1 as shown in solid circles in Figure 12 and the time t1 in

Figure 13 collision detection finds that there is a potential collision between the pink

tool and the orange tool The dynamic priority assignment is executed for the pink tool

and the orange tool according to their traverse speeds A higher priority is therefore

assigned to the pink tool which is at a higher traverse speed This allows the pink tool

to continue deposition along its original path while the orange tool with a lower

priority waits at the far end of its current hatch line until the potential collision is

eliminated As collision detection is executed at the predefined rate the potential

collision between the pink tool and the orange tool has been eliminated some time after

t1 Hence they can again deposit materials concurrently as shown in Figure 13 some

time after t1 Meanwhile it can be noticed that the blue tool and the grey tool have

already completed their respective tasks

At time t2 as shown in dashed circles in Figure 12 and time t2 in Figure 13 a potential

collision is detected between the pink tool and the orange tool again Contrary to the

case at t1 the pink tool now traverses at a lower speed than the orange tool because the

lengths of hatch lines of the pink contour are much longer than that of the orange one

The dynamic priority assignment is executed again for the pink tool and the orange

tool in the order of their traverse speeds Thus a higher priority is assigned to the

orange tool which is at a higher traverse speed The orange tool continues to deposit

material along its original path while the pink tool with a lower priority waits until the

Figure 13 X-t graph of the selected layer of the human ear model

t2

Potential collision detected

dynamic priority

assignment executed

t1

22

potential collision is eliminated Some time after t2 the potential collision between

the pink tool and the orange tool is found to have been eliminated This pair can again

deposit materials concurrently as shown in Figure 13 some time after t2 When the

pink tool finishes its task this layer is completed The digital fabrication process of

the selected layer of the ear model is shown in Figure 14

(a) Before time t1 all tools deposit

concurrently

Torange Tpink Tblue

Tgrey

Tpink Torange

(b) At time t1 pink tool continues to

deposit while the orange tool waits

(e) At time after t2 pink tool and orange

tool continue to deposit concurrently to

complete the layer

Torange Tpink

(c) At time between t1 and t2 pink tool

and orange tool deposit concurrently

(d) At time t2 orange tool continues to

deposit while pink tool waits

Torange Torange Tpink Tpink

Figure 14 Digital fabrication of the selected

layer of the human ear model

23

To suit different material properties and fabrication requirements it is assumed that the

deposition speed of the orange tool is increased from 15mms-1

to 20mms-1

Figure 15

shows X-t graph of the ear model layer with increased deposition speed for the orange

tool In this case the pink tool can never catch up with the orange tool Hence four

tools can deposit concurrently to complete the layer Figure 16 compares the build

times of the human ear model by different toolpath planning approaches For

consistency the deposition speeds of tools in all the approaches are VP =20mms-1

VO =15mms-1

VB =5mms-1

and VG=5mms-1

It can be seen that the proposed dynamic

priority-based approach improves the efficiency by 32 19 and 18 respectively

Figure 15 X-t graph of the ear model layer with increased

deposition speed of the orange tool

Figure 16 Comparison of build times of the human ear model

by different toolpath planning approaches

24

in comparison with the sequential approach the entire envelope-based approach [20]

and the separate envelope-based approach [26] The entire envelope-based and the

separate envelope-based approaches are characterised by the construction of bounding

envelopes around slice contours by offsetting outward a distance of the tool radius

Overlap test is executed for these envelopes and tools are not allowed to move

concurrently when the associated contour envelopes overlapped For example the

orange tool in Figure 12 cannot move until the pink tool completes the pink part

The proposed dynamic priority-based approach eliminates this constraint It constructs

envelopes around the tools directly rather than around the slice contours Relative

positions of tools are monitored at a predefined rate It enhances concurrency of tool

motions by assigning tool motion priorities to avoid collision This highlights the

effectiveness of the proposed approach in improving the fabrication efficiency of

biomedical objects

42 A Toy Tank

A tank model with dimensions of 225mm x 78mm x 96mm as shown in Figure 17 is

processed below to demonstrate possible applications of the proposed work in

development of complex toy products The model is sliced into 480 layers Figure 18

shows a layer of the tank to be made of four materials represented in black green red

and orange The deposition speeds of the four tools of the same radius R=10mm are

set to be VB =20mms-1

VG =15mms-1

VO =15mms-1

and VR=10mms-1

for the black

green orange and red tools respectively

Figure 17 A toy tank model

Slicing

plane

25

At the beginning since the collision detection algorithm finds that the orange tool will

collide with the black tool the orange tool with lower traverse speed is commanded to

start deposition after the potential collision is eliminated So at first the black red and

green tools move concurrently to deposit their specific materials Some time later at t1

a potential collision is detected between the black tool and the green tool as shown in

solid circles in Figure 18 and time t1 in Figure 19 The motion priorities of the black

tool and the green tool are assigned according to their traverse speeds The black tool

which is at a higher traverse speed is assigned with a higher priority and thus

continues material deposition along its original path together with the orange tool

while the green tool with a lower priority pauses to give way until the potential

collision is eliminated Some time after t1 the green tool the black tool and the orange

tool can again deposit materials concurrently to complete this layer The digital

fabrication process of the selected layer of the tank model is shown in Figure 20

t1

Potential collision detected

dynamic priority assignment

executed

Figure 19 X-t graph of the selected layer of tank model

Y

X O Figure 18 A selected layer of the tank model

VxG VG

VB VxB

Red tool

Orange tool

26

Figure 21 compares the build times of the tank model by different toolpath planning

approaches It can be seen that the proposed dynamic priority-based approach

improves the efficiency by 62 51 and 43 respectively in comparison with the

previous approaches This highlights that the effectiveness of the proposed approach to

improve the fabrication efficiency of relatively complex objects and to shorten the

product development cycle accordingly

Figure 21 Comparison of build times of the tank model

by different toolpath planning approaches

Figure 20 Digital fabrication of the selected layer of the tank model

(c) Black tool orange tool and green tool

deposit concurrently

to complete this layer

Tgreen

Tblack

Torange

(a) Concurrent deposition by black

tool red tool and green tool

(b) Orange tool starts Black tool continues

to deposit while green tool waits

Tred Tblack

Tgreen Tgreen

Tblack

Torange

27

5 Conclusion and Future Work

This paper presents an approach to concurrent toolpath planning to improve the

fabrication efficiency of MMLM The approach incorporates decoupled motion

planning technique for multiple moving objects with a collision detection algorithm

and a dynamic priority assignment scheme It is characterised by construction of

envelopes directly around individual tools which are treated as multiple moving

objects while the dynamic priority assignment scheme coordinates the tool motions to

avoid collisions The proposed approach has been integrated with a multi-material

virtual prototyping system and digital fabrication of prototypes for biomedical

applications and product development shows that it can substantially shorten the

fabrication time of relatively complex multi-material objects The approach can be

adapted for process control of MMLM when appropriate hardware becomes available

Nevertheless some further developments are deemed beneficial Firstly as the

proposed approach now adopts only up-and-down zigzags for internal contour filling

it would be useful to include the spiral contour filling mode which is also a common

contour filling strategy in LM This may require modifying the algorithms for tool

collision detection and motion coordination accordingly

Secondly tool collision detection in the proposed approach is a real-time process being

executed at a predefined rate It seems that pausing a tool to avoid collision may

possibly impair the smoothness of the fabrication process Although attempt has been

made to reduce such effect by holding the tool only at the far end of the current hatch

line after it is completed it may be worthwhile to further improve the fabrication

process In this connection it would perhaps be beneficial to take advantage of the X-t

graph (tool displacements versus time) which shows the locations and times of

possible tool collisions during the complete fabrication process of a layer to eliminate

tool pauses X-t graphs for all layers would first be generated off-line from which the

locations and times of possible tool collisions could be pre-loaded into the computer

for prior coordination of tool motions For example the start time of a tool could be

suitably adjusted to avoid potential collisions instead of halting the tools during

fabrication Indeed this off-line planning would reduce the computation requirements

during digital or physical fabrication particularly for large and complex objects

28

Thirdly the impact of the proposed toolpath planning approach on fabrication quality

needs further investigation Shrinkage and warpage of prototypes may be affected by

the adopted toolpath planning strategy It would be desirable to study the relationship

between the toolpath planning strategy and the prototype quality

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[2] Wohlers TT Wohlers Report 2009 Wohlers Associates Inc 2009

[3] Kulkarni P Marsan A and Dutta D A review of process planning techniques

in layered manufacturing Rapid Prototyping Journal 2000 6(1) 18-35

[4] Kochan A Rapid prototyping gains speed volume and precision Rapid

Prototyping Journal 2000 20(4)295-299

[5] Bellini A Fused deposition of ceramics a comprehensive experimental

analytical and computational study of material behaviour fabrication process and

equipment design PhD thesis Drexel University USA 2002

[6] Hauser C Dunschen M Egan M and Sutcliffe C Transformation algorithms

for image preparation in spiral growth manufacturing (SGM) Rapid Prototyping

Journal 2008 14(4)188-196

[7] Sintermask Technologies httpwwwsintermaskcompagephpp=8 2007

[8] Voxeljet

httpwwwvoxeljetdevoxeljet_eninhaltprodukte3d-drucksystemeuberblickp

hpnavid=6 2007

[9] Erasenthiran P and Beal VE Functionally graded materials In Hopkinson N

et al editors Rapid manufacturing an industrial revolution for the digital age

John Wiley amp Sons Ltd 2006 pp103-124

[10] Khalil S Nam F and Sun W Multi-nozzle deposition for construction of 3D

biopolymer tissue scaffolds Rapid Prototyping Journal 2005 11(1) 9-17

[11] Kumar V Solid modeling and algorithms for heterogeneous objects PhD

thesis Drexel University USA 1999

[12] Qiu D Langrana NA Danforth SC Safari A and Jafari M Intelligent

toolpath for extrusion-based LM process Rapid Prototyping Journal 2001 7(1)

18-23

[13] Jepson LR Multiple material selective laser sintering PhD thesis The

University of Texas at Austin USA 2002

[14] Cho W Sachs EM Patrikalakis NM and Troxel DE A dithering algorithm

for local composition control with three-dimensional printing Computer-Aided

Design 2003 35(9) 851-867

[15] Cesarano III J Direct-write fabrication with fine particle suspensions

Advanced Materials and Processes 2005 163(8) 49-56

[16] Inamdar A Magana M Medina F Grajeda Y and Wicker R Development

of an automated multiple material stereolithography machine In Bourell DL et

al editors Solid Freeform Fabrication Symposium 2006 University of Texas at

Austin USA 2006 pp 624-635

[17] Wang J and Shaw LL Fabrication of functionally graded materials via inkjet

22

potential collision is eliminated Some time after t2 the potential collision between

the pink tool and the orange tool is found to have been eliminated This pair can again

deposit materials concurrently as shown in Figure 13 some time after t2 When the

pink tool finishes its task this layer is completed The digital fabrication process of

the selected layer of the ear model is shown in Figure 14

(a) Before time t1 all tools deposit

concurrently

Torange Tpink Tblue

Tgrey

Tpink Torange

(b) At time t1 pink tool continues to

deposit while the orange tool waits

(e) At time after t2 pink tool and orange

tool continue to deposit concurrently to

complete the layer

Torange Tpink

(c) At time between t1 and t2 pink tool

and orange tool deposit concurrently

(d) At time t2 orange tool continues to

deposit while pink tool waits

Torange Torange Tpink Tpink

Figure 14 Digital fabrication of the selected

layer of the human ear model

23

To suit different material properties and fabrication requirements it is assumed that the

deposition speed of the orange tool is increased from 15mms-1

to 20mms-1

Figure 15

shows X-t graph of the ear model layer with increased deposition speed for the orange

tool In this case the pink tool can never catch up with the orange tool Hence four

tools can deposit concurrently to complete the layer Figure 16 compares the build

times of the human ear model by different toolpath planning approaches For

consistency the deposition speeds of tools in all the approaches are VP =20mms-1

VO =15mms-1

VB =5mms-1

and VG=5mms-1

It can be seen that the proposed dynamic

priority-based approach improves the efficiency by 32 19 and 18 respectively

Figure 15 X-t graph of the ear model layer with increased

deposition speed of the orange tool

Figure 16 Comparison of build times of the human ear model

by different toolpath planning approaches

24

in comparison with the sequential approach the entire envelope-based approach [20]

and the separate envelope-based approach [26] The entire envelope-based and the

separate envelope-based approaches are characterised by the construction of bounding

envelopes around slice contours by offsetting outward a distance of the tool radius

Overlap test is executed for these envelopes and tools are not allowed to move

concurrently when the associated contour envelopes overlapped For example the

orange tool in Figure 12 cannot move until the pink tool completes the pink part

The proposed dynamic priority-based approach eliminates this constraint It constructs

envelopes around the tools directly rather than around the slice contours Relative

positions of tools are monitored at a predefined rate It enhances concurrency of tool

motions by assigning tool motion priorities to avoid collision This highlights the

effectiveness of the proposed approach in improving the fabrication efficiency of

biomedical objects

42 A Toy Tank

A tank model with dimensions of 225mm x 78mm x 96mm as shown in Figure 17 is

processed below to demonstrate possible applications of the proposed work in

development of complex toy products The model is sliced into 480 layers Figure 18

shows a layer of the tank to be made of four materials represented in black green red

and orange The deposition speeds of the four tools of the same radius R=10mm are

set to be VB =20mms-1

VG =15mms-1

VO =15mms-1

and VR=10mms-1

for the black

green orange and red tools respectively

Figure 17 A toy tank model

Slicing

plane

25

At the beginning since the collision detection algorithm finds that the orange tool will

collide with the black tool the orange tool with lower traverse speed is commanded to

start deposition after the potential collision is eliminated So at first the black red and

green tools move concurrently to deposit their specific materials Some time later at t1

a potential collision is detected between the black tool and the green tool as shown in

solid circles in Figure 18 and time t1 in Figure 19 The motion priorities of the black

tool and the green tool are assigned according to their traverse speeds The black tool

which is at a higher traverse speed is assigned with a higher priority and thus

continues material deposition along its original path together with the orange tool

while the green tool with a lower priority pauses to give way until the potential

collision is eliminated Some time after t1 the green tool the black tool and the orange

tool can again deposit materials concurrently to complete this layer The digital

fabrication process of the selected layer of the tank model is shown in Figure 20

t1

Potential collision detected

dynamic priority assignment

executed

Figure 19 X-t graph of the selected layer of tank model

Y

X O Figure 18 A selected layer of the tank model

VxG VG

VB VxB

Red tool

Orange tool

26

Figure 21 compares the build times of the tank model by different toolpath planning

approaches It can be seen that the proposed dynamic priority-based approach

improves the efficiency by 62 51 and 43 respectively in comparison with the

previous approaches This highlights that the effectiveness of the proposed approach to

improve the fabrication efficiency of relatively complex objects and to shorten the

product development cycle accordingly

Figure 21 Comparison of build times of the tank model

by different toolpath planning approaches

Figure 20 Digital fabrication of the selected layer of the tank model

(c) Black tool orange tool and green tool

deposit concurrently

to complete this layer

Tgreen

Tblack

Torange

(a) Concurrent deposition by black

tool red tool and green tool

(b) Orange tool starts Black tool continues

to deposit while green tool waits

Tred Tblack

Tgreen Tgreen

Tblack

Torange

27

5 Conclusion and Future Work

This paper presents an approach to concurrent toolpath planning to improve the

fabrication efficiency of MMLM The approach incorporates decoupled motion

planning technique for multiple moving objects with a collision detection algorithm

and a dynamic priority assignment scheme It is characterised by construction of

envelopes directly around individual tools which are treated as multiple moving

objects while the dynamic priority assignment scheme coordinates the tool motions to

avoid collisions The proposed approach has been integrated with a multi-material

virtual prototyping system and digital fabrication of prototypes for biomedical

applications and product development shows that it can substantially shorten the

fabrication time of relatively complex multi-material objects The approach can be

adapted for process control of MMLM when appropriate hardware becomes available

Nevertheless some further developments are deemed beneficial Firstly as the

proposed approach now adopts only up-and-down zigzags for internal contour filling

it would be useful to include the spiral contour filling mode which is also a common

contour filling strategy in LM This may require modifying the algorithms for tool

collision detection and motion coordination accordingly

Secondly tool collision detection in the proposed approach is a real-time process being

executed at a predefined rate It seems that pausing a tool to avoid collision may

possibly impair the smoothness of the fabrication process Although attempt has been

made to reduce such effect by holding the tool only at the far end of the current hatch

line after it is completed it may be worthwhile to further improve the fabrication

process In this connection it would perhaps be beneficial to take advantage of the X-t

graph (tool displacements versus time) which shows the locations and times of

possible tool collisions during the complete fabrication process of a layer to eliminate

tool pauses X-t graphs for all layers would first be generated off-line from which the

locations and times of possible tool collisions could be pre-loaded into the computer

for prior coordination of tool motions For example the start time of a tool could be

suitably adjusted to avoid potential collisions instead of halting the tools during

fabrication Indeed this off-line planning would reduce the computation requirements

during digital or physical fabrication particularly for large and complex objects

28

Thirdly the impact of the proposed toolpath planning approach on fabrication quality

needs further investigation Shrinkage and warpage of prototypes may be affected by

the adopted toolpath planning strategy It would be desirable to study the relationship

between the toolpath planning strategy and the prototype quality

6 References

[1] Hopkinson N Hague RJM and Dickens PM Rapid manufacturing an

industrial revolution for the digital age John Wiley amp Sons Ltd 2006

[2] Wohlers TT Wohlers Report 2009 Wohlers Associates Inc 2009

[3] Kulkarni P Marsan A and Dutta D A review of process planning techniques

in layered manufacturing Rapid Prototyping Journal 2000 6(1) 18-35

[4] Kochan A Rapid prototyping gains speed volume and precision Rapid

Prototyping Journal 2000 20(4)295-299

[5] Bellini A Fused deposition of ceramics a comprehensive experimental

analytical and computational study of material behaviour fabrication process and

equipment design PhD thesis Drexel University USA 2002

[6] Hauser C Dunschen M Egan M and Sutcliffe C Transformation algorithms

for image preparation in spiral growth manufacturing (SGM) Rapid Prototyping

Journal 2008 14(4)188-196

[7] Sintermask Technologies httpwwwsintermaskcompagephpp=8 2007

[8] Voxeljet

httpwwwvoxeljetdevoxeljet_eninhaltprodukte3d-drucksystemeuberblickp

hpnavid=6 2007

[9] Erasenthiran P and Beal VE Functionally graded materials In Hopkinson N

et al editors Rapid manufacturing an industrial revolution for the digital age

John Wiley amp Sons Ltd 2006 pp103-124

[10] Khalil S Nam F and Sun W Multi-nozzle deposition for construction of 3D

biopolymer tissue scaffolds Rapid Prototyping Journal 2005 11(1) 9-17

[11] Kumar V Solid modeling and algorithms for heterogeneous objects PhD

thesis Drexel University USA 1999

[12] Qiu D Langrana NA Danforth SC Safari A and Jafari M Intelligent

toolpath for extrusion-based LM process Rapid Prototyping Journal 2001 7(1)

18-23

[13] Jepson LR Multiple material selective laser sintering PhD thesis The

University of Texas at Austin USA 2002

[14] Cho W Sachs EM Patrikalakis NM and Troxel DE A dithering algorithm

for local composition control with three-dimensional printing Computer-Aided

Design 2003 35(9) 851-867

[15] Cesarano III J Direct-write fabrication with fine particle suspensions

Advanced Materials and Processes 2005 163(8) 49-56

[16] Inamdar A Magana M Medina F Grajeda Y and Wicker R Development

of an automated multiple material stereolithography machine In Bourell DL et

al editors Solid Freeform Fabrication Symposium 2006 University of Texas at

Austin USA 2006 pp 624-635

[17] Wang J and Shaw LL Fabrication of functionally graded materials via inkjet

23

To suit different material properties and fabrication requirements it is assumed that the

deposition speed of the orange tool is increased from 15mms-1

to 20mms-1

Figure 15

shows X-t graph of the ear model layer with increased deposition speed for the orange

tool In this case the pink tool can never catch up with the orange tool Hence four

tools can deposit concurrently to complete the layer Figure 16 compares the build

times of the human ear model by different toolpath planning approaches For

consistency the deposition speeds of tools in all the approaches are VP =20mms-1

VO =15mms-1

VB =5mms-1

and VG=5mms-1

It can be seen that the proposed dynamic

priority-based approach improves the efficiency by 32 19 and 18 respectively

Figure 15 X-t graph of the ear model layer with increased

deposition speed of the orange tool

Figure 16 Comparison of build times of the human ear model

by different toolpath planning approaches

24

in comparison with the sequential approach the entire envelope-based approach [20]

and the separate envelope-based approach [26] The entire envelope-based and the

separate envelope-based approaches are characterised by the construction of bounding

envelopes around slice contours by offsetting outward a distance of the tool radius

Overlap test is executed for these envelopes and tools are not allowed to move

concurrently when the associated contour envelopes overlapped For example the

orange tool in Figure 12 cannot move until the pink tool completes the pink part

The proposed dynamic priority-based approach eliminates this constraint It constructs

envelopes around the tools directly rather than around the slice contours Relative

positions of tools are monitored at a predefined rate It enhances concurrency of tool

motions by assigning tool motion priorities to avoid collision This highlights the

effectiveness of the proposed approach in improving the fabrication efficiency of

biomedical objects

42 A Toy Tank

A tank model with dimensions of 225mm x 78mm x 96mm as shown in Figure 17 is

processed below to demonstrate possible applications of the proposed work in

development of complex toy products The model is sliced into 480 layers Figure 18

shows a layer of the tank to be made of four materials represented in black green red

and orange The deposition speeds of the four tools of the same radius R=10mm are

set to be VB =20mms-1

VG =15mms-1

VO =15mms-1

and VR=10mms-1

for the black

green orange and red tools respectively

Figure 17 A toy tank model

Slicing

plane

25

At the beginning since the collision detection algorithm finds that the orange tool will

collide with the black tool the orange tool with lower traverse speed is commanded to

start deposition after the potential collision is eliminated So at first the black red and

green tools move concurrently to deposit their specific materials Some time later at t1

a potential collision is detected between the black tool and the green tool as shown in

solid circles in Figure 18 and time t1 in Figure 19 The motion priorities of the black

tool and the green tool are assigned according to their traverse speeds The black tool

which is at a higher traverse speed is assigned with a higher priority and thus

continues material deposition along its original path together with the orange tool

while the green tool with a lower priority pauses to give way until the potential

collision is eliminated Some time after t1 the green tool the black tool and the orange

tool can again deposit materials concurrently to complete this layer The digital

fabrication process of the selected layer of the tank model is shown in Figure 20

t1

Potential collision detected

dynamic priority assignment

executed

Figure 19 X-t graph of the selected layer of tank model

Y

X O Figure 18 A selected layer of the tank model

VxG VG

VB VxB

Red tool

Orange tool

26

Figure 21 compares the build times of the tank model by different toolpath planning

approaches It can be seen that the proposed dynamic priority-based approach

improves the efficiency by 62 51 and 43 respectively in comparison with the

previous approaches This highlights that the effectiveness of the proposed approach to

improve the fabrication efficiency of relatively complex objects and to shorten the

product development cycle accordingly

Figure 21 Comparison of build times of the tank model

by different toolpath planning approaches

Figure 20 Digital fabrication of the selected layer of the tank model

(c) Black tool orange tool and green tool

deposit concurrently

to complete this layer

Tgreen

Tblack

Torange

(a) Concurrent deposition by black

tool red tool and green tool

(b) Orange tool starts Black tool continues

to deposit while green tool waits

Tred Tblack

Tgreen Tgreen

Tblack

Torange

27

5 Conclusion and Future Work

This paper presents an approach to concurrent toolpath planning to improve the

fabrication efficiency of MMLM The approach incorporates decoupled motion

planning technique for multiple moving objects with a collision detection algorithm

and a dynamic priority assignment scheme It is characterised by construction of

envelopes directly around individual tools which are treated as multiple moving

objects while the dynamic priority assignment scheme coordinates the tool motions to

avoid collisions The proposed approach has been integrated with a multi-material

virtual prototyping system and digital fabrication of prototypes for biomedical

applications and product development shows that it can substantially shorten the

fabrication time of relatively complex multi-material objects The approach can be

adapted for process control of MMLM when appropriate hardware becomes available

Nevertheless some further developments are deemed beneficial Firstly as the

proposed approach now adopts only up-and-down zigzags for internal contour filling

it would be useful to include the spiral contour filling mode which is also a common

contour filling strategy in LM This may require modifying the algorithms for tool

collision detection and motion coordination accordingly

Secondly tool collision detection in the proposed approach is a real-time process being

executed at a predefined rate It seems that pausing a tool to avoid collision may

possibly impair the smoothness of the fabrication process Although attempt has been

made to reduce such effect by holding the tool only at the far end of the current hatch

line after it is completed it may be worthwhile to further improve the fabrication

process In this connection it would perhaps be beneficial to take advantage of the X-t

graph (tool displacements versus time) which shows the locations and times of

possible tool collisions during the complete fabrication process of a layer to eliminate

tool pauses X-t graphs for all layers would first be generated off-line from which the

locations and times of possible tool collisions could be pre-loaded into the computer

for prior coordination of tool motions For example the start time of a tool could be

suitably adjusted to avoid potential collisions instead of halting the tools during

fabrication Indeed this off-line planning would reduce the computation requirements

during digital or physical fabrication particularly for large and complex objects

28

Thirdly the impact of the proposed toolpath planning approach on fabrication quality

needs further investigation Shrinkage and warpage of prototypes may be affected by

the adopted toolpath planning strategy It would be desirable to study the relationship

between the toolpath planning strategy and the prototype quality

6 References

[1] Hopkinson N Hague RJM and Dickens PM Rapid manufacturing an

industrial revolution for the digital age John Wiley amp Sons Ltd 2006

[2] Wohlers TT Wohlers Report 2009 Wohlers Associates Inc 2009

[3] Kulkarni P Marsan A and Dutta D A review of process planning techniques

in layered manufacturing Rapid Prototyping Journal 2000 6(1) 18-35

[4] Kochan A Rapid prototyping gains speed volume and precision Rapid

Prototyping Journal 2000 20(4)295-299

[5] Bellini A Fused deposition of ceramics a comprehensive experimental

analytical and computational study of material behaviour fabrication process and

equipment design PhD thesis Drexel University USA 2002

[6] Hauser C Dunschen M Egan M and Sutcliffe C Transformation algorithms

for image preparation in spiral growth manufacturing (SGM) Rapid Prototyping

Journal 2008 14(4)188-196

[7] Sintermask Technologies httpwwwsintermaskcompagephpp=8 2007

[8] Voxeljet

httpwwwvoxeljetdevoxeljet_eninhaltprodukte3d-drucksystemeuberblickp

hpnavid=6 2007

[9] Erasenthiran P and Beal VE Functionally graded materials In Hopkinson N

et al editors Rapid manufacturing an industrial revolution for the digital age

John Wiley amp Sons Ltd 2006 pp103-124

[10] Khalil S Nam F and Sun W Multi-nozzle deposition for construction of 3D

biopolymer tissue scaffolds Rapid Prototyping Journal 2005 11(1) 9-17

[11] Kumar V Solid modeling and algorithms for heterogeneous objects PhD

thesis Drexel University USA 1999

[12] Qiu D Langrana NA Danforth SC Safari A and Jafari M Intelligent

toolpath for extrusion-based LM process Rapid Prototyping Journal 2001 7(1)

18-23

[13] Jepson LR Multiple material selective laser sintering PhD thesis The

University of Texas at Austin USA 2002

[14] Cho W Sachs EM Patrikalakis NM and Troxel DE A dithering algorithm

for local composition control with three-dimensional printing Computer-Aided

Design 2003 35(9) 851-867

[15] Cesarano III J Direct-write fabrication with fine particle suspensions

Advanced Materials and Processes 2005 163(8) 49-56

[16] Inamdar A Magana M Medina F Grajeda Y and Wicker R Development

of an automated multiple material stereolithography machine In Bourell DL et

al editors Solid Freeform Fabrication Symposium 2006 University of Texas at

Austin USA 2006 pp 624-635

[17] Wang J and Shaw LL Fabrication of functionally graded materials via inkjet

24

in comparison with the sequential approach the entire envelope-based approach [20]

and the separate envelope-based approach [26] The entire envelope-based and the

separate envelope-based approaches are characterised by the construction of bounding

envelopes around slice contours by offsetting outward a distance of the tool radius

Overlap test is executed for these envelopes and tools are not allowed to move

concurrently when the associated contour envelopes overlapped For example the

orange tool in Figure 12 cannot move until the pink tool completes the pink part

The proposed dynamic priority-based approach eliminates this constraint It constructs

envelopes around the tools directly rather than around the slice contours Relative

positions of tools are monitored at a predefined rate It enhances concurrency of tool

motions by assigning tool motion priorities to avoid collision This highlights the

effectiveness of the proposed approach in improving the fabrication efficiency of

biomedical objects

42 A Toy Tank

A tank model with dimensions of 225mm x 78mm x 96mm as shown in Figure 17 is

processed below to demonstrate possible applications of the proposed work in

development of complex toy products The model is sliced into 480 layers Figure 18

shows a layer of the tank to be made of four materials represented in black green red

and orange The deposition speeds of the four tools of the same radius R=10mm are

set to be VB =20mms-1

VG =15mms-1

VO =15mms-1

and VR=10mms-1

for the black

green orange and red tools respectively

Figure 17 A toy tank model

Slicing

plane

25

At the beginning since the collision detection algorithm finds that the orange tool will

collide with the black tool the orange tool with lower traverse speed is commanded to

start deposition after the potential collision is eliminated So at first the black red and

green tools move concurrently to deposit their specific materials Some time later at t1

a potential collision is detected between the black tool and the green tool as shown in

solid circles in Figure 18 and time t1 in Figure 19 The motion priorities of the black

tool and the green tool are assigned according to their traverse speeds The black tool

which is at a higher traverse speed is assigned with a higher priority and thus

continues material deposition along its original path together with the orange tool

while the green tool with a lower priority pauses to give way until the potential

collision is eliminated Some time after t1 the green tool the black tool and the orange

tool can again deposit materials concurrently to complete this layer The digital

fabrication process of the selected layer of the tank model is shown in Figure 20

t1

Potential collision detected

dynamic priority assignment

executed

Figure 19 X-t graph of the selected layer of tank model

Y

X O Figure 18 A selected layer of the tank model

VxG VG

VB VxB

Red tool

Orange tool

26

Figure 21 compares the build times of the tank model by different toolpath planning

approaches It can be seen that the proposed dynamic priority-based approach

improves the efficiency by 62 51 and 43 respectively in comparison with the

previous approaches This highlights that the effectiveness of the proposed approach to

improve the fabrication efficiency of relatively complex objects and to shorten the

product development cycle accordingly

Figure 21 Comparison of build times of the tank model

by different toolpath planning approaches

Figure 20 Digital fabrication of the selected layer of the tank model

(c) Black tool orange tool and green tool

deposit concurrently

to complete this layer

Tgreen

Tblack

Torange

(a) Concurrent deposition by black

tool red tool and green tool

(b) Orange tool starts Black tool continues

to deposit while green tool waits

Tred Tblack

Tgreen Tgreen

Tblack

Torange

27

5 Conclusion and Future Work

This paper presents an approach to concurrent toolpath planning to improve the

fabrication efficiency of MMLM The approach incorporates decoupled motion

planning technique for multiple moving objects with a collision detection algorithm

and a dynamic priority assignment scheme It is characterised by construction of

envelopes directly around individual tools which are treated as multiple moving

objects while the dynamic priority assignment scheme coordinates the tool motions to

avoid collisions The proposed approach has been integrated with a multi-material

virtual prototyping system and digital fabrication of prototypes for biomedical

applications and product development shows that it can substantially shorten the

fabrication time of relatively complex multi-material objects The approach can be

adapted for process control of MMLM when appropriate hardware becomes available

Nevertheless some further developments are deemed beneficial Firstly as the

proposed approach now adopts only up-and-down zigzags for internal contour filling

it would be useful to include the spiral contour filling mode which is also a common

contour filling strategy in LM This may require modifying the algorithms for tool

collision detection and motion coordination accordingly

Secondly tool collision detection in the proposed approach is a real-time process being

executed at a predefined rate It seems that pausing a tool to avoid collision may

possibly impair the smoothness of the fabrication process Although attempt has been

made to reduce such effect by holding the tool only at the far end of the current hatch

line after it is completed it may be worthwhile to further improve the fabrication

process In this connection it would perhaps be beneficial to take advantage of the X-t

graph (tool displacements versus time) which shows the locations and times of

possible tool collisions during the complete fabrication process of a layer to eliminate

tool pauses X-t graphs for all layers would first be generated off-line from which the

locations and times of possible tool collisions could be pre-loaded into the computer

for prior coordination of tool motions For example the start time of a tool could be

suitably adjusted to avoid potential collisions instead of halting the tools during

fabrication Indeed this off-line planning would reduce the computation requirements

during digital or physical fabrication particularly for large and complex objects

28

Thirdly the impact of the proposed toolpath planning approach on fabrication quality

needs further investigation Shrinkage and warpage of prototypes may be affected by

the adopted toolpath planning strategy It would be desirable to study the relationship

between the toolpath planning strategy and the prototype quality

6 References

[1] Hopkinson N Hague RJM and Dickens PM Rapid manufacturing an

industrial revolution for the digital age John Wiley amp Sons Ltd 2006

[2] Wohlers TT Wohlers Report 2009 Wohlers Associates Inc 2009

[3] Kulkarni P Marsan A and Dutta D A review of process planning techniques

in layered manufacturing Rapid Prototyping Journal 2000 6(1) 18-35

[4] Kochan A Rapid prototyping gains speed volume and precision Rapid

Prototyping Journal 2000 20(4)295-299

[5] Bellini A Fused deposition of ceramics a comprehensive experimental

analytical and computational study of material behaviour fabrication process and

equipment design PhD thesis Drexel University USA 2002

[6] Hauser C Dunschen M Egan M and Sutcliffe C Transformation algorithms

for image preparation in spiral growth manufacturing (SGM) Rapid Prototyping

Journal 2008 14(4)188-196

[7] Sintermask Technologies httpwwwsintermaskcompagephpp=8 2007

[8] Voxeljet

httpwwwvoxeljetdevoxeljet_eninhaltprodukte3d-drucksystemeuberblickp

hpnavid=6 2007

[9] Erasenthiran P and Beal VE Functionally graded materials In Hopkinson N

et al editors Rapid manufacturing an industrial revolution for the digital age

John Wiley amp Sons Ltd 2006 pp103-124

[10] Khalil S Nam F and Sun W Multi-nozzle deposition for construction of 3D

biopolymer tissue scaffolds Rapid Prototyping Journal 2005 11(1) 9-17

[11] Kumar V Solid modeling and algorithms for heterogeneous objects PhD

thesis Drexel University USA 1999

[12] Qiu D Langrana NA Danforth SC Safari A and Jafari M Intelligent

toolpath for extrusion-based LM process Rapid Prototyping Journal 2001 7(1)

18-23

[13] Jepson LR Multiple material selective laser sintering PhD thesis The

University of Texas at Austin USA 2002

[14] Cho W Sachs EM Patrikalakis NM and Troxel DE A dithering algorithm

for local composition control with three-dimensional printing Computer-Aided

Design 2003 35(9) 851-867

[15] Cesarano III J Direct-write fabrication with fine particle suspensions

Advanced Materials and Processes 2005 163(8) 49-56

[16] Inamdar A Magana M Medina F Grajeda Y and Wicker R Development

of an automated multiple material stereolithography machine In Bourell DL et

al editors Solid Freeform Fabrication Symposium 2006 University of Texas at

Austin USA 2006 pp 624-635

[17] Wang J and Shaw LL Fabrication of functionally graded materials via inkjet

25

At the beginning since the collision detection algorithm finds that the orange tool will

collide with the black tool the orange tool with lower traverse speed is commanded to

start deposition after the potential collision is eliminated So at first the black red and

green tools move concurrently to deposit their specific materials Some time later at t1

a potential collision is detected between the black tool and the green tool as shown in

solid circles in Figure 18 and time t1 in Figure 19 The motion priorities of the black

tool and the green tool are assigned according to their traverse speeds The black tool

which is at a higher traverse speed is assigned with a higher priority and thus

continues material deposition along its original path together with the orange tool

while the green tool with a lower priority pauses to give way until the potential

collision is eliminated Some time after t1 the green tool the black tool and the orange

tool can again deposit materials concurrently to complete this layer The digital

fabrication process of the selected layer of the tank model is shown in Figure 20

t1

Potential collision detected

dynamic priority assignment

executed

Figure 19 X-t graph of the selected layer of tank model

Y

X O Figure 18 A selected layer of the tank model

VxG VG

VB VxB

Red tool

Orange tool

26

Figure 21 compares the build times of the tank model by different toolpath planning

approaches It can be seen that the proposed dynamic priority-based approach

improves the efficiency by 62 51 and 43 respectively in comparison with the

previous approaches This highlights that the effectiveness of the proposed approach to

improve the fabrication efficiency of relatively complex objects and to shorten the

product development cycle accordingly

Figure 21 Comparison of build times of the tank model

by different toolpath planning approaches

Figure 20 Digital fabrication of the selected layer of the tank model

(c) Black tool orange tool and green tool

deposit concurrently

to complete this layer

Tgreen

Tblack

Torange

(a) Concurrent deposition by black

tool red tool and green tool

(b) Orange tool starts Black tool continues

to deposit while green tool waits

Tred Tblack

Tgreen Tgreen

Tblack

Torange

27

5 Conclusion and Future Work

This paper presents an approach to concurrent toolpath planning to improve the

fabrication efficiency of MMLM The approach incorporates decoupled motion

planning technique for multiple moving objects with a collision detection algorithm

and a dynamic priority assignment scheme It is characterised by construction of

envelopes directly around individual tools which are treated as multiple moving

objects while the dynamic priority assignment scheme coordinates the tool motions to

avoid collisions The proposed approach has been integrated with a multi-material

virtual prototyping system and digital fabrication of prototypes for biomedical

applications and product development shows that it can substantially shorten the

fabrication time of relatively complex multi-material objects The approach can be

adapted for process control of MMLM when appropriate hardware becomes available

Nevertheless some further developments are deemed beneficial Firstly as the

proposed approach now adopts only up-and-down zigzags for internal contour filling

it would be useful to include the spiral contour filling mode which is also a common

contour filling strategy in LM This may require modifying the algorithms for tool

collision detection and motion coordination accordingly

Secondly tool collision detection in the proposed approach is a real-time process being

executed at a predefined rate It seems that pausing a tool to avoid collision may

possibly impair the smoothness of the fabrication process Although attempt has been

made to reduce such effect by holding the tool only at the far end of the current hatch

line after it is completed it may be worthwhile to further improve the fabrication

process In this connection it would perhaps be beneficial to take advantage of the X-t

graph (tool displacements versus time) which shows the locations and times of

possible tool collisions during the complete fabrication process of a layer to eliminate

tool pauses X-t graphs for all layers would first be generated off-line from which the

locations and times of possible tool collisions could be pre-loaded into the computer

for prior coordination of tool motions For example the start time of a tool could be

suitably adjusted to avoid potential collisions instead of halting the tools during

fabrication Indeed this off-line planning would reduce the computation requirements

during digital or physical fabrication particularly for large and complex objects

28

Thirdly the impact of the proposed toolpath planning approach on fabrication quality

needs further investigation Shrinkage and warpage of prototypes may be affected by

the adopted toolpath planning strategy It would be desirable to study the relationship

between the toolpath planning strategy and the prototype quality

6 References

[1] Hopkinson N Hague RJM and Dickens PM Rapid manufacturing an

industrial revolution for the digital age John Wiley amp Sons Ltd 2006

[2] Wohlers TT Wohlers Report 2009 Wohlers Associates Inc 2009

[3] Kulkarni P Marsan A and Dutta D A review of process planning techniques

in layered manufacturing Rapid Prototyping Journal 2000 6(1) 18-35

[4] Kochan A Rapid prototyping gains speed volume and precision Rapid

Prototyping Journal 2000 20(4)295-299

[5] Bellini A Fused deposition of ceramics a comprehensive experimental

analytical and computational study of material behaviour fabrication process and

equipment design PhD thesis Drexel University USA 2002

[6] Hauser C Dunschen M Egan M and Sutcliffe C Transformation algorithms

for image preparation in spiral growth manufacturing (SGM) Rapid Prototyping

Journal 2008 14(4)188-196

[7] Sintermask Technologies httpwwwsintermaskcompagephpp=8 2007

[8] Voxeljet

httpwwwvoxeljetdevoxeljet_eninhaltprodukte3d-drucksystemeuberblickp

hpnavid=6 2007

[9] Erasenthiran P and Beal VE Functionally graded materials In Hopkinson N

et al editors Rapid manufacturing an industrial revolution for the digital age

John Wiley amp Sons Ltd 2006 pp103-124

[10] Khalil S Nam F and Sun W Multi-nozzle deposition for construction of 3D

biopolymer tissue scaffolds Rapid Prototyping Journal 2005 11(1) 9-17

[11] Kumar V Solid modeling and algorithms for heterogeneous objects PhD

thesis Drexel University USA 1999

[12] Qiu D Langrana NA Danforth SC Safari A and Jafari M Intelligent

toolpath for extrusion-based LM process Rapid Prototyping Journal 2001 7(1)

18-23

[13] Jepson LR Multiple material selective laser sintering PhD thesis The

University of Texas at Austin USA 2002

[14] Cho W Sachs EM Patrikalakis NM and Troxel DE A dithering algorithm

for local composition control with three-dimensional printing Computer-Aided

Design 2003 35(9) 851-867

[15] Cesarano III J Direct-write fabrication with fine particle suspensions

Advanced Materials and Processes 2005 163(8) 49-56

[16] Inamdar A Magana M Medina F Grajeda Y and Wicker R Development

of an automated multiple material stereolithography machine In Bourell DL et

al editors Solid Freeform Fabrication Symposium 2006 University of Texas at

Austin USA 2006 pp 624-635

[17] Wang J and Shaw LL Fabrication of functionally graded materials via inkjet

26

Figure 21 compares the build times of the tank model by different toolpath planning

approaches It can be seen that the proposed dynamic priority-based approach

improves the efficiency by 62 51 and 43 respectively in comparison with the

previous approaches This highlights that the effectiveness of the proposed approach to

improve the fabrication efficiency of relatively complex objects and to shorten the

product development cycle accordingly

Figure 21 Comparison of build times of the tank model

by different toolpath planning approaches

Figure 20 Digital fabrication of the selected layer of the tank model

(c) Black tool orange tool and green tool

deposit concurrently

to complete this layer

Tgreen

Tblack

Torange

(a) Concurrent deposition by black

tool red tool and green tool

(b) Orange tool starts Black tool continues

to deposit while green tool waits

Tred Tblack

Tgreen Tgreen

Tblack

Torange

27

5 Conclusion and Future Work

This paper presents an approach to concurrent toolpath planning to improve the

fabrication efficiency of MMLM The approach incorporates decoupled motion

planning technique for multiple moving objects with a collision detection algorithm

and a dynamic priority assignment scheme It is characterised by construction of

envelopes directly around individual tools which are treated as multiple moving

objects while the dynamic priority assignment scheme coordinates the tool motions to

avoid collisions The proposed approach has been integrated with a multi-material

virtual prototyping system and digital fabrication of prototypes for biomedical

applications and product development shows that it can substantially shorten the

fabrication time of relatively complex multi-material objects The approach can be

adapted for process control of MMLM when appropriate hardware becomes available

Nevertheless some further developments are deemed beneficial Firstly as the

proposed approach now adopts only up-and-down zigzags for internal contour filling

it would be useful to include the spiral contour filling mode which is also a common

contour filling strategy in LM This may require modifying the algorithms for tool

collision detection and motion coordination accordingly

Secondly tool collision detection in the proposed approach is a real-time process being

executed at a predefined rate It seems that pausing a tool to avoid collision may

possibly impair the smoothness of the fabrication process Although attempt has been

made to reduce such effect by holding the tool only at the far end of the current hatch

line after it is completed it may be worthwhile to further improve the fabrication

process In this connection it would perhaps be beneficial to take advantage of the X-t

graph (tool displacements versus time) which shows the locations and times of

possible tool collisions during the complete fabrication process of a layer to eliminate

tool pauses X-t graphs for all layers would first be generated off-line from which the

locations and times of possible tool collisions could be pre-loaded into the computer

for prior coordination of tool motions For example the start time of a tool could be

suitably adjusted to avoid potential collisions instead of halting the tools during

fabrication Indeed this off-line planning would reduce the computation requirements

during digital or physical fabrication particularly for large and complex objects

28

Thirdly the impact of the proposed toolpath planning approach on fabrication quality

needs further investigation Shrinkage and warpage of prototypes may be affected by

the adopted toolpath planning strategy It would be desirable to study the relationship

between the toolpath planning strategy and the prototype quality

6 References

[1] Hopkinson N Hague RJM and Dickens PM Rapid manufacturing an

industrial revolution for the digital age John Wiley amp Sons Ltd 2006

[2] Wohlers TT Wohlers Report 2009 Wohlers Associates Inc 2009

[3] Kulkarni P Marsan A and Dutta D A review of process planning techniques

in layered manufacturing Rapid Prototyping Journal 2000 6(1) 18-35

[4] Kochan A Rapid prototyping gains speed volume and precision Rapid

Prototyping Journal 2000 20(4)295-299

[5] Bellini A Fused deposition of ceramics a comprehensive experimental

analytical and computational study of material behaviour fabrication process and

equipment design PhD thesis Drexel University USA 2002

[6] Hauser C Dunschen M Egan M and Sutcliffe C Transformation algorithms

for image preparation in spiral growth manufacturing (SGM) Rapid Prototyping

Journal 2008 14(4)188-196

[7] Sintermask Technologies httpwwwsintermaskcompagephpp=8 2007

[8] Voxeljet

httpwwwvoxeljetdevoxeljet_eninhaltprodukte3d-drucksystemeuberblickp

hpnavid=6 2007

[9] Erasenthiran P and Beal VE Functionally graded materials In Hopkinson N

et al editors Rapid manufacturing an industrial revolution for the digital age

John Wiley amp Sons Ltd 2006 pp103-124

[10] Khalil S Nam F and Sun W Multi-nozzle deposition for construction of 3D

biopolymer tissue scaffolds Rapid Prototyping Journal 2005 11(1) 9-17

[11] Kumar V Solid modeling and algorithms for heterogeneous objects PhD

thesis Drexel University USA 1999

[12] Qiu D Langrana NA Danforth SC Safari A and Jafari M Intelligent

toolpath for extrusion-based LM process Rapid Prototyping Journal 2001 7(1)

18-23

[13] Jepson LR Multiple material selective laser sintering PhD thesis The

University of Texas at Austin USA 2002

[14] Cho W Sachs EM Patrikalakis NM and Troxel DE A dithering algorithm

for local composition control with three-dimensional printing Computer-Aided

Design 2003 35(9) 851-867

[15] Cesarano III J Direct-write fabrication with fine particle suspensions

Advanced Materials and Processes 2005 163(8) 49-56

[16] Inamdar A Magana M Medina F Grajeda Y and Wicker R Development

of an automated multiple material stereolithography machine In Bourell DL et

al editors Solid Freeform Fabrication Symposium 2006 University of Texas at

Austin USA 2006 pp 624-635

[17] Wang J and Shaw LL Fabrication of functionally graded materials via inkjet

27

5 Conclusion and Future Work

This paper presents an approach to concurrent toolpath planning to improve the

fabrication efficiency of MMLM The approach incorporates decoupled motion

planning technique for multiple moving objects with a collision detection algorithm

and a dynamic priority assignment scheme It is characterised by construction of

envelopes directly around individual tools which are treated as multiple moving

objects while the dynamic priority assignment scheme coordinates the tool motions to

avoid collisions The proposed approach has been integrated with a multi-material

virtual prototyping system and digital fabrication of prototypes for biomedical

applications and product development shows that it can substantially shorten the

fabrication time of relatively complex multi-material objects The approach can be

adapted for process control of MMLM when appropriate hardware becomes available

Nevertheless some further developments are deemed beneficial Firstly as the

proposed approach now adopts only up-and-down zigzags for internal contour filling

it would be useful to include the spiral contour filling mode which is also a common

contour filling strategy in LM This may require modifying the algorithms for tool

collision detection and motion coordination accordingly

Secondly tool collision detection in the proposed approach is a real-time process being

executed at a predefined rate It seems that pausing a tool to avoid collision may

possibly impair the smoothness of the fabrication process Although attempt has been

made to reduce such effect by holding the tool only at the far end of the current hatch

line after it is completed it may be worthwhile to further improve the fabrication

process In this connection it would perhaps be beneficial to take advantage of the X-t

graph (tool displacements versus time) which shows the locations and times of

possible tool collisions during the complete fabrication process of a layer to eliminate

tool pauses X-t graphs for all layers would first be generated off-line from which the

locations and times of possible tool collisions could be pre-loaded into the computer

for prior coordination of tool motions For example the start time of a tool could be

suitably adjusted to avoid potential collisions instead of halting the tools during

fabrication Indeed this off-line planning would reduce the computation requirements

during digital or physical fabrication particularly for large and complex objects

28

Thirdly the impact of the proposed toolpath planning approach on fabrication quality

needs further investigation Shrinkage and warpage of prototypes may be affected by

the adopted toolpath planning strategy It would be desirable to study the relationship

between the toolpath planning strategy and the prototype quality

6 References

[1] Hopkinson N Hague RJM and Dickens PM Rapid manufacturing an

industrial revolution for the digital age John Wiley amp Sons Ltd 2006

[2] Wohlers TT Wohlers Report 2009 Wohlers Associates Inc 2009

[3] Kulkarni P Marsan A and Dutta D A review of process planning techniques

in layered manufacturing Rapid Prototyping Journal 2000 6(1) 18-35

[4] Kochan A Rapid prototyping gains speed volume and precision Rapid

Prototyping Journal 2000 20(4)295-299

[5] Bellini A Fused deposition of ceramics a comprehensive experimental

analytical and computational study of material behaviour fabrication process and

equipment design PhD thesis Drexel University USA 2002

[6] Hauser C Dunschen M Egan M and Sutcliffe C Transformation algorithms

for image preparation in spiral growth manufacturing (SGM) Rapid Prototyping

Journal 2008 14(4)188-196

[7] Sintermask Technologies httpwwwsintermaskcompagephpp=8 2007

[8] Voxeljet

httpwwwvoxeljetdevoxeljet_eninhaltprodukte3d-drucksystemeuberblickp

hpnavid=6 2007

[9] Erasenthiran P and Beal VE Functionally graded materials In Hopkinson N

et al editors Rapid manufacturing an industrial revolution for the digital age

John Wiley amp Sons Ltd 2006 pp103-124

[10] Khalil S Nam F and Sun W Multi-nozzle deposition for construction of 3D

biopolymer tissue scaffolds Rapid Prototyping Journal 2005 11(1) 9-17

[11] Kumar V Solid modeling and algorithms for heterogeneous objects PhD

thesis Drexel University USA 1999

[12] Qiu D Langrana NA Danforth SC Safari A and Jafari M Intelligent

toolpath for extrusion-based LM process Rapid Prototyping Journal 2001 7(1)

18-23

[13] Jepson LR Multiple material selective laser sintering PhD thesis The

University of Texas at Austin USA 2002

[14] Cho W Sachs EM Patrikalakis NM and Troxel DE A dithering algorithm

for local composition control with three-dimensional printing Computer-Aided

Design 2003 35(9) 851-867

[15] Cesarano III J Direct-write fabrication with fine particle suspensions

Advanced Materials and Processes 2005 163(8) 49-56

[16] Inamdar A Magana M Medina F Grajeda Y and Wicker R Development

of an automated multiple material stereolithography machine In Bourell DL et

al editors Solid Freeform Fabrication Symposium 2006 University of Texas at

Austin USA 2006 pp 624-635

[17] Wang J and Shaw LL Fabrication of functionally graded materials via inkjet

28

Thirdly the impact of the proposed toolpath planning approach on fabrication quality

needs further investigation Shrinkage and warpage of prototypes may be affected by

the adopted toolpath planning strategy It would be desirable to study the relationship

between the toolpath planning strategy and the prototype quality

6 References

[1] Hopkinson N Hague RJM and Dickens PM Rapid manufacturing an

industrial revolution for the digital age John Wiley amp Sons Ltd 2006

[2] Wohlers TT Wohlers Report 2009 Wohlers Associates Inc 2009

[3] Kulkarni P Marsan A and Dutta D A review of process planning techniques

in layered manufacturing Rapid Prototyping Journal 2000 6(1) 18-35

[4] Kochan A Rapid prototyping gains speed volume and precision Rapid

Prototyping Journal 2000 20(4)295-299

[5] Bellini A Fused deposition of ceramics a comprehensive experimental

analytical and computational study of material behaviour fabrication process and

equipment design PhD thesis Drexel University USA 2002

[6] Hauser C Dunschen M Egan M and Sutcliffe C Transformation algorithms

for image preparation in spiral growth manufacturing (SGM) Rapid Prototyping

Journal 2008 14(4)188-196

[7] Sintermask Technologies httpwwwsintermaskcompagephpp=8 2007

[8] Voxeljet

httpwwwvoxeljetdevoxeljet_eninhaltprodukte3d-drucksystemeuberblickp

hpnavid=6 2007

[9] Erasenthiran P and Beal VE Functionally graded materials In Hopkinson N

et al editors Rapid manufacturing an industrial revolution for the digital age

John Wiley amp Sons Ltd 2006 pp103-124

[10] Khalil S Nam F and Sun W Multi-nozzle deposition for construction of 3D

biopolymer tissue scaffolds Rapid Prototyping Journal 2005 11(1) 9-17

[11] Kumar V Solid modeling and algorithms for heterogeneous objects PhD

thesis Drexel University USA 1999

[12] Qiu D Langrana NA Danforth SC Safari A and Jafari M Intelligent

toolpath for extrusion-based LM process Rapid Prototyping Journal 2001 7(1)

18-23

[13] Jepson LR Multiple material selective laser sintering PhD thesis The

University of Texas at Austin USA 2002

[14] Cho W Sachs EM Patrikalakis NM and Troxel DE A dithering algorithm

for local composition control with three-dimensional printing Computer-Aided

Design 2003 35(9) 851-867

[15] Cesarano III J Direct-write fabrication with fine particle suspensions

Advanced Materials and Processes 2005 163(8) 49-56

[16] Inamdar A Magana M Medina F Grajeda Y and Wicker R Development

of an automated multiple material stereolithography machine In Bourell DL et

al editors Solid Freeform Fabrication Symposium 2006 University of Texas at

Austin USA 2006 pp 624-635

[17] Wang J and Shaw LL Fabrication of functionally graded materials via inkjet

29

color printing Journal of American Ceramics Society 2006 89(10) 3285-3289

[18] Malone E Berry M and Lipson H Freeform fabrication and characterization

of zinc-air batteries Rapid Prototyping Journal 2008 14(3)128-140

[19] Objet Geometries Ltd httpwwwobjetcom3D-PrinterConnex350 2009

[20] Choi SH and Cheung HH A topological hierarchy-based approach to

toolpath planning for multi-material layered manufacturing Computer-Aided

Design 2006 38(2)143-156

[21] Liang JS and Lin AC System development off adaptive spraying paths for

rapid prototyping Rapid Prototyping Journal 2003 9(5)289-300

[22] Sun Q Rizvi GM Bellehumeur CT and Gu P Effect of processing

conditions on the bonding quality of FDM polymer filaments Rapid Prototyping

Journal 2008 14(2) 72-80

[23] Zhu WM and Yu KM Tool path generation of multi-material assembly for

rapid manufacture Rapid Prototyping Journal 2002 8(5)277-283

[24] Zhou MY Path Planning of functionally graded material objects for layered

manufacturing International Journal of Production Research 2004

42(2)405-415

[25] Choi SH and Cheung HH A multi-material virtual prototyping system

Computer-Aided Design 2005 37(1)123-136

[26] Choi SH and Zhu WK Efficient concurrent toolpath planning for

multi-material layered manufacturing In Bourell DL et al editors Solid

Freeform Fabrication Symposium 2008 University of Texas at Austin USA

2008 pp 429-440

[27] Ericson C Real-Time Collision Detection Elsevier Inc 2005

[28] Jimenez P Thomas F and Torras C 3D collision detection a survey

Computers and Graphics 2000 25269-285

[29] Laumond JP Kineo CAM a success story of motion planning algorithm IEEE

Robotics and Automation Magazine 2006 13(2)90-93

[30] Wagner IA Altshuler Y Yanovski V and Bruckstein AM Cooperative

cleaners a study in ant robotics The International Journal of Robotics Research

2008 27(1) 127-151

[31] Li TY and Latombe JC On-line manipulation planning for two robot arms in

a dynamic environment The International Journal of Robotics Research 1997

16(2)144-167

[32] Peasgood M Clark CM and McPhee J A complete and scalable strategy for

coordinating multiple robots within roadmaps IEEE Transactions On Robotics

2008 24(2) 283-292

[33] Lavalle SM Planning algorithms Cambridge Press 2006

[34] Todt E Raush G and Suarez R Analysis and classification of multiple robot

coordination methods In Proceedings of the IEEE International Conference on

Robotics and Automation San Francisco California USA 2000 pp3158-3163

[35] Bennewitz M Burgard W and Thrun S Finding and optimizing solvable

priority schemes for decoupled path planning techniques for teams of mobile

robots Robotics and Autonomous Systems 2002 41(2-3)89-99

[36] Hopcroft JE Schwartz JT and Sharir M On the complexity of motion

planning for multiple independent objects PSPACE-hardness of the

bdquowarehouseman‟s problem‟ International Journal of Robotics Research 1984

3(4)76ndash88

[37] Lavalle SM and Hutchinson SA Optimal motion planning for multiple robots

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having independent goals IEEE Transactions on Robotics and Automation 1998

14(3) 912-925

[38] Lee KH and Kim JH Multi-robot cooperation-based mobile printer system

Robotics and Autonomous Systems 2006 54(3)193-204

[39] Peng J and Akella S Coordinating multiple robots with kinodynamic

constraints along specified paths International Journal of Robotics Research

2005 24(4) 295ndash310

[40] Rekleitist I Shuet VL New AP and Choset H Limited communication

multi-robot team based coverage In Proceedings of International Conference on

Robotics and Automation New Orleans Louisiana USA 2004 pp3462-3468

[41] Lee BJ Lee SO and Park GT Trajectory generation and motion tracking

control for the robot soccer game In Proceedings of the IEEE International

Conference on Intelligent Robots and Systems Kyongju South Korea 1999

vol2 pp 1149-1154

[42] Chang C Chung MJ and Lee BH Collision avoidance of two general robot

manipulators by minimum delay time IEEE Transaction On Systems Man and

Cybernetics 1994 24(3) 517-522

[43] van den Berg J and Overmars M Prioritized motion planning for multiple

robots In Proceedings of IEEERSJ International Conference on Intelligent

Robots and Systems 2005 pp 2217ndash2222

[44] Erdmann M A and Lozano-Perez T On multiple moving objects

Algorithmica 1987 2477-521

[45] Ferrari C Pagello E Ota J and Arai T Multirobot motion coordination in

space and time Robotics and Autonomous Systems 1998 25 219ndash229

[46] Azarm K and Schmidt G A decentralized approach for the conflict-free motion

of multiple mobile robots In Proceedings of the IEEERSJ International

Conference on Intelligent Robots and Systems (IROS) 1996 pp 1667ndash1674

[47] Clark CM Bretl T and Rock S Applying kinodynamic randomized motion

planning with a dynamic priority system to multi-robot space systems In

Proceedings of IEEE Aerospace Conference 2002 vol7 pp 3621- 3631

[48] Choi SH and Cheung HH A versatile virtual prototyping system for rapid

product development Computers in Industry 2008 59(5)477-488